You can pair your Logitech G903 LIGHTSPEED Wireless Mouse with any Logitech LIGHTSPEED USB Receiver (but not with other Logitech receivers, like the Bolt or Unifying receivers.)
To pair your mouse with a new receiver (of the correct type!) you would use the Logitech Connection Utility https://support.logi.com/hc/en-my/articles/360025141574 (or possibly also using Logitech G HUB as outlined in https://support.logi.com/hc/en-us/articles/7709072311959)
Answer from Yisroel Tech on Stack ExchangeNew Unifying Receiver - how to pair without cables.
Logitech MX Anywhere 2S - Bluetooth or Unifying Receiver questions...
How do I connect a my Logitech unifying receiver keyboard/mouse to my macOS 12 mac? - Ask Different
How do I pair a Logitech mouse to a different Logitech unifying receiver?
Videos
You can pair your Logitech G903 LIGHTSPEED Wireless Mouse with any Logitech LIGHTSPEED USB Receiver (but not with other Logitech receivers, like the Bolt or Unifying receivers.)
To pair your mouse with a new receiver (of the correct type!) you would use the Logitech Connection Utility https://support.logi.com/hc/en-my/articles/360025141574 (or possibly also using Logitech G HUB as outlined in https://support.logi.com/hc/en-us/articles/7709072311959)
Logitech Unify mice, keyboards and tranceivers can be re-paired (in arbitrary combinations) using a utility that can be downloaded from Logitech.
In some cases a (non-Unify) mouse or keyboard can be re-paired with a another receiver from the same model/series, but as far as I know that was only valid for very old models (>15 years old). And the required pairing utilities (series specific) don't work on recent Windows versions (Windows 7 was the last one I think) and are very hard to find (not available from Logitech anymore).
For all other Logitech devices it can't be done.
Your G903 is not a Unify model and there doesn't seem to be a pairing utility available on the Logitech web-site for this model, so I think you are out of luck on this one.
I have a new unifying receiver i'm trying to pair with existing logitech devices on my desktop, but they're both wireless. I can't use the pairing software, as I can't use the mouse or keyboard.
I have a separate work laptop - which won't let me install the software.
I want to configure a unifiying receiver on each device, which I can then use the same keyboard and mouse on both (mx keys and anywhere 2) using the multiple device functionality.
How would i get this to work?
I have one receiver which works for both, but I can't configure the second one.
Thanks in advance!
forgot to mention
it may be the fact that my Bluetooth dongle was just a cheapy but I find the signal is weak if plugged into the rear usb ports (assume its the metal case between dongle and user) the unifying receiver has no such problem. - plugged in at back and forgotten
is it worth extra expense? No! (IMO)
I have a keyboard and mouse with the unifying receiver - it just works, never had an issue. plug it in, setup mouse and keyboard the way I want and forget it, I have changed batteries, turned them off etc. turn it on again and it just works.
I also have a Bluetooth dongle sat in the drawer I occasionally use it for other devices.
you can set it up now with the unifying receiver that you have and change your mind later if you get a Bluetooth dongle (you wont)
the logitech software is not really needed, windows will find drivers from microsoft, but the software does give that extra bit of customisation.