Are the later versions backward compatible? i.e. can I replace the failed module from my 12/2009 with 04/2012 or whatever the nearest dealer has?

P.S. Not sure what exactly caused it, but I had the battery disconnected as a safety precaution while fixing backup camera, and now get "Lighting System" error that doesn't allow car to move as it thinks the driver door is open (plus a myriad of other things not working).
Rheingold test says FRM isn't responding, so I assume it's shot.