I think your neighbour should keep the lovely Ozzie indoors for at least a week, whether he's an indoor or outdoor cat. Then he gets used to new smells.
If she can accompany him for his first couple of trips after that period - and bring him in with her. Hopefully Ozzie wont go wandering to his old home again - he just has to readjust to his new home. Patience and love will hopefully help your neighbour.

Lynne