Well, there is a theory that the Moon was blasted from the Earth by a big chunk of impacting something...
Well, that is the idea. If there was life on earth at the time, a smaller earth than we have at present since it collided with and absorbed with something the size of Mars, there could well be fossils on the moon. There might be nothing left of those fossils on earth, but the moon could have preserved them. Kind of interesting.
I can't imagine any fossils surviving that kind of impact, the heat would have been incredible. Just MHO though.