The context is copied from a parent to a child. In your case context.obj for cli() which you do not expose in your example, is None. The None is copied into the child context for fn1() and fn2(), but then in fn1() you change the copy to 1. Finally, in fn2() you receive a copy of the context for cli() in which obj is still None

So to achieve your desired result there are (at least) two options.

1. Make context.obj on the parent context a mutable object, and then mutate said object
2. As you indicated was possible, directly access the parent context via something like ctx.parent.obj = 1

An example of the first (my preferred) method:

Example

import click, sys


@click.group(chain=True)
@click.pass_context
def cli(ctx) -> None:
    ctx.obj = {}


@cli.command()
@click.pass_context
def fn1(ctx):
    ctx.obj['fn1'] = 1


@cli.command()
@click.pass_context
def fn2(ctx):
    click.echo(f'obj: {ctx.obj}')

Test Code

if __name__ == "__main__":
    print('Click Version: {}'.format(click.__version__))
    print('Python Version: {}'.format(sys.version))
    print('-----------')
    cmd = 'fn1 fn2'
    print('> ' + cmd)
    cli(cmd.split())

Results:

Click Version: 8.1.3
Python Version: 3.7.8 (tags/v3.7.8:4b47a5b6ba, Jun 28 2020, 08:53:46) [MSC v.1916 64 bit (AMD64)]
-----------
> fn1 fn2
obj: {'fn1': 1}

If you can edit your click command functions, you can organize them like this:

@cli.command()
@click.argument('some_argument', type=str)
@click.pass_context
def say_something(ctx, some_argument):
    return _say_something(ctx, some_argument):

def _say_something(ctx, some_argument):
    print(some_argument)

If built like this, then you can call _say_something() function as an undecorated (normal) Python function.

If you can not edit your commands

Building on this answer you can pass the context to another click command using this function:

Code:

def call_click_command_with_ctx(cmd, ctx, *args, **kwargs):
    """ Wrapper to call a click command with a Context object

    :param cmd: click cli command function to call
    :param ctx: click context
    :param args: arguments to pass to the function
    :param kwargs: keyword arguments to pass to the function
    :return: None
    """

    # monkey patch make_context
    def make_context(*some_args, **some_kwargs):
        child_ctx = click.Context(cmd, parent=ctx)
        with child_ctx.scope(cleanup=False):
            cmd.parse_args(child_ctx, list(args))
        return child_ctx

    cmd.make_context = make_context
    prev_make_context = cmd.make_context

    # call the command
    call_click_command(cmd, *args, **kwargs)

    # restore make_context
    cmd.make_context = prev_make_context

How does this work?

This works because click is a well designed OO framework. The @click.Command object can be introspected to determine what parameters it is expecting. Then a command line can be constructed that will look like the command line that click is expecting. In addition, the make_context method of the command can be overridden to allow the command context to used by the command.

Code from Previous Answer:

def call_click_command(cmd, *args, **kwargs):
    """ Wrapper to call a click command

    :param cmd: click cli command function to call
    :param args: arguments to pass to the function
    :param kwargs: keywrod arguments to pass to the function
    :return: None
    """

    # Get positional arguments from args
    arg_values = {c.name: a for a, c in zip(args, cmd.params)}
    args_needed = {c.name: c for c in cmd.params
                   if c.name not in arg_values}

    # build and check opts list from kwargs
    opts = {a.name: a for a in cmd.params if isinstance(a, click.Option)}
    for name in kwargs:
        if name in opts:
            arg_values[name] = kwargs[name]
        else:
            if name in args_needed:
                arg_values[name] = kwargs[name]
                del args_needed[name]
            else:
                raise click.BadParameter(
                    "Unknown keyword argument '{}'".format(name))


    # check positional arguments list
    for arg in (a for a in cmd.params if isinstance(a, click.Argument)):
        if arg.name not in arg_values:
            raise click.BadParameter("Missing required positional"
                                     "parameter '{}'".format(arg.name))

    # build parameter lists
    opts_list = sum(
        [[o.opts[0], str(arg_values[n])] for n, o in opts.items()], [])
    args_list = [str(v) for n, v in arg_values.items() if n not in opts]

    # call the command
    cmd(opts_list + args_list)

Test Code:

import click

@click.group(chain=True)
@click.option('--some_common_option', type=float, default=1e-10)
@click.pass_context
def cli(ctx, some_common_option):
    # save shared params within context object for different commands
    for k, v in locals().items():
        if 'ctx' not in k:
            ctx.obj[k] = v


@cli.command()
@click.argument('some_argument', type=str)
@click.pass_context
def say_something(ctx, some_argument):
    print(some_argument)


@cli.command()
@click.argument('some_other_argument', type=str)
@click.pass_context
def say_more(ctx, some_other_argument):
    ctx.obj['text'] = some_other_argument
    call_click_command_with_ctx(say_something, ctx, ctx.obj['text'])


if __name__ == "__main__":
    commands = (
        'say_something something',
        'say_more more',
        '--help',
    )

    import sys, time

    time.sleep(1)
    print('Click Version: {}'.format(click.__version__))
    print('Python Version: {}'.format(sys.version))
    for cmd in commands:
        try:
            time.sleep(0.1)
            print('-----------')
            print('> ' + cmd)
            time.sleep(0.1)
            cli(cmd.split(), obj={})

        except BaseException as exc:
            if str(exc) != '0' and \
                    not isinstance(exc, (click.ClickException, SystemExit)):
                raise

Results:

Click Version: 6.7
Python Version: 3.6.3 (v3.6.3:2c5fed8, Oct  3 2017, 18:11:49) [MSC v.1900 64 bit (AMD64)]
-----------
> say_something something
something
-----------
> say_more more
more
-----------
> --help
Usage: test.py [OPTIONS] COMMAND1 [ARGS]... [COMMAND2 [ARGS]...]...

Options:
  --some_common_option FLOAT
  --help                      Show this message and exit.

Commands:
  say_more
  say_something

find_object will search object in parent context by type. If you want to use multiple objects the easiest way is to make obj a dictionary. Here example:

@click.group
@click.option('-c', 'config')
@click.pass_context
def cli(ctx, config):
    if ctx.obj is None:
        ctx.obj = dict()
    # add any data to obj here...
    ctx.obj['a'] = 'example_A'
    ctx.obj['b'] = 'example_B'

@cli.command()
@click.pass_context()
def cmd_a(ctx):
  # check prepared data
  print(ctx.obj['a'])

@cli.command()
@cli.pass_context()
def cmd_b(ctx):
  # check prepared data
  print(ctx.obj['b'])

Slightly different way - use custom class for obj:

class Config(object):

    def __init__(self, config):
        # do something with config here ...
        self.a = 'example_A'
        self.b = 'example_B'

# in your def cli()
ctx.obj = Config(config)
# in your commands you can works with your prepared data like this:
print(ctx.obj.a)
print(ctx.obj.b)

Hope this helps.

You would directly pass your Config instance as keyword argument obj to runner.invoke:

import click
from click.testing import CliRunner

class Config():
    def __init__(self):
        self.value = 651

@click.command()
@click.pass_obj
def print_numberinfo(obj):
    if not hasattr(obj, 'value'):
        obj = Config()
    click.echo(obj.value)

def test_print_numberinfo():
    obj = Config()
    obj.value = 777
    runner = CliRunner()
    # how do I pass ctx to runner.invoke?
    result = runner.invoke(print_numberinfo, obj=obj)
    assert result.output == str(obj.value) + '\n'

I would suggest adding a @staticmethod to your Config class to use as the target of the callback like:

Callback Method:

@staticmethod
def click_callback(ctx, param, value):
    getattr(ctx.obj, ctx.obj.func_name)()
    return value

Test Code:

import click

class Config:
    def __init__(self, func_name):
        self.func_name = func_name

    def func_a(self):
        click.echo('Func A')

    def func_b(self):
        click.echo('Func B')

    @staticmethod
    def click_callback(ctx, param, value):
        getattr(ctx.obj, ctx.obj.func_name)()
        return value


@click.group()
@click.option('-f', '--func-name', required=True)
@click.pass_context
def group(ctx, func_name):
    ctx.obj = Config(func_name)


@group.command()
@click.option('--my-option', '-o', callback=Config.click_callback)
def command(my_option):
    click.echo('command: {}'.format(my_option))


if __name__ == "__main__":
    commands = (
        '-f func_a command -o optionA',
        '-f func_b command -o optionB',
        '-f func_a command -o ',
        'command',
        '--help',
        '',
    )

    import sys, time

    time.sleep(1)
    print('Click Version: {}'.format(click.__version__))
    print('Python Version: {}'.format(sys.version))
    for cmd in commands:
        try:
            time.sleep(0.1)
            print('-----------')
            print('> ' + cmd)
            time.sleep(0.1)
            group(cmd.split())

        except BaseException as exc:
            if str(exc) != '0' and \
                    not isinstance(exc, (click.ClickException, SystemExit)):
                raise

Results:

Click Version: 6.7
Python Version: 3.6.3 (v3.6.3:2c5fed8, Oct  3 2017, 18:11:49) [MSC v.1900 64 bit (AMD64)]
-----------
> -f func_a command -o optionA
Func A
command: optionA
-----------
> -f func_b command -o optionB
Func B
command: optionB
-----------
> -f func_a command -o 
Error: -o option requires an argument
-----------
> command
Usage: test.py [OPTIONS] COMMAND [ARGS]...

Error: Missing option "-f" / "--func-name".
-----------
> --help
Usage: test.py [OPTIONS] COMMAND [ARGS]...

Options:
  -f, --func-name TEXT  [required]
  --help                Show this message and exit.

Commands:
  command
-----------
> 
Usage: test.py [OPTIONS] COMMAND [ARGS]...

Options:
  -f, --func-name TEXT  [required]
  --help                Show this message and exit.

Commands:
  command

https://click.palletsprojects.com/en/7.x/complex/

Add @click.pass_context as the final decorator and it becomes the first parameter in your function.