There seem to be many links and other such stuff, but no actual code using pipes. The advantage of using java.io.PipedInputStream and java.io.PipedOutputStream is that there is no additional consumption of memory. ByteArrayOutputStream.toByteArray() returns a copy of the original buffer, so that means that whatever you have in memory, you now have two copies of it. Then writing to an InputStream means you now have three copies of the data.

The code using lambdas (hat-tip to @John Manko from the comments):

PipedInputStream in = new PipedInputStream();
final PipedOutputStream out = new PipedOutputStream(in);
// in a background thread, write the given output stream to the
// PipedOutputStream for consumption
new Thread(() -> {originalOutputStream.writeTo(out);}).start();

One thing that @John Manko noted is that in certain cases, when you don't have control of the creation of the OutputStream, you may end up in a situation where the creator may clean up the OutputStream object prematurely. If you are getting the ClosedPipeException, then you should try inverting the constructors:

PipedInputStream in = new PipedInputStream(out);
new Thread(() -> {originalOutputStream.writeTo(out);}).start();

Note you can invert the constructors for the examples below too.

Thanks also to @AlexK for correcting me with starting a Thread instead of just kicking off a Runnable.

The code using try-with-resources:

// take the copy of the stream and re-write it to an InputStream
PipedInputStream in = new PipedInputStream();
    new Thread(new Runnable() {
        public void run () {
            // try-with-resources here
            // putting the try block outside the Thread will cause the
            // PipedOutputStream resource to close before the Runnable finishes
            try (final PipedOutputStream out = new PipedOutputStream(in)) {
                // write the original OutputStream to the PipedOutputStream
                // note that in order for the below method to work, you need
                // to ensure that the data has finished writing to the
                // ByteArrayOutputStream
                originalByteArrayOutputStream.writeTo(out);
            }
            catch (IOException e) {
                // logging and exception handling should go here
            }
        }
    }).start();

The original code I wrote:

// take the copy of the stream and re-write it to an InputStream
PipedInputStream in = new PipedInputStream();
final PipedOutputStream out = new PipedOutputStream(in);
new Thread(new Runnable() {
    public void run () {
        try {
            // write the original OutputStream to the PipedOutputStream
            // note that in order for the below method to work, you need
            // to ensure that the data has finished writing to the
            // ByteArrayOutputStream
            originalByteArrayOutputStream.writeTo(out);
        }
        catch (IOException e) {
            // logging and exception handling should go here
        }
        finally {
            // close the PipedOutputStream here because we're done writing data
            // once this thread has completed its run
            if (out != null) {
                // close the PipedOutputStream cleanly
                out.close();
            }
        }   
    }
}).start();

This code assumes that the originalByteArrayOutputStream is a ByteArrayOutputStream as it is usually the only usable output stream, unless you're writing to a file. The great thing about this is that since it's in a separate thread, it also is working in parallel, so whatever is consuming your input stream will be streaming out of your old output stream too. That is beneficial because the buffer can remain smaller and you'll have less latency and less memory usage.

If you don't have a ByteArrayOutputStream, then instead of using writeTo(), you will have to use one of the write() methods in the java.io.OutputStream class or one of the other methods available in a subclass.

As WMR mentioned, org.apache.commons.io.IOUtils from Apache has a method called copy(InputStream,OutputStream) which does exactly what you're looking for.

So, you have:

InputStream in;
OutputStream out;
IOUtils.copy(in,out);
in.close();
out.close();

...in your code.

Is there a reason you're avoiding IOUtils?