I would say, if you can, CATCH the neighbor's cat (maybe try a long-handled fishing net?) and then call the neighbor and ask if they know where their cat is. When they snottily say that it is at home, "of course", then ask them if they are willing to bet money on it. Tell them that you will call animal control if the cat is ever in your yard again - they can install the "cat fencing" stuff that goes up and then creates an overhang, preventing cats from climbing the fence. They don't like it? Then they can bail their cat out of the pound...
