Tell your neighbor to try giving the cat a toy with the owner's scent on it. By this I mean something as simple as a sock that has been worn, but not washed, made into a ball. Cut off top of sock and stuff into toe and knot or sew shut. Give this to the cat to sleep with and play with and have near him when the owner is not around. I hope this works. Some cats suffer from terrible "seperation anxiety" and this helps them have the one they miss close to them by proxy.
Let me know if this helps and I will try to come up with some other things for them to try.
Happy to have you with us at The Cat Site.
I am sure some of the other members will have more suggestions, also.