I for one wouldn't let my GF ride the bike after all this. Imagine this scenario:
1) Bike stolen
2) Bike sold to this current guy who thinks he owns it legitimately
3) You steal it and give it to GF
4) This guy sees her riding it, stops her, beats her teeth out and takes it back because he thinks she stole it.
You are assuming and risking too much. If you were going to be riding it I'd say do what you like, but in this case you are risking your girl.