This question was asked on cardgamedb, and I didn't have a solid answer for it:
My opponent has Ser Edmure Tully (TCP) and uses his ability to shuffle an event back into his deck. I then play Melisandre's Favor on Edmure. Can I trigger his ability to shuffle something back into my deck? Nobody knew whether the 'Limit once per round' restriction on his ability applies to the copy of Edmure or to the player who currently controls him.
Granted, the FAQ entry I found doesn't mention control changes, but it does say: