[Noney]

I just dealt with this exact same problem -- this is an easy one.

First, you must do the right thing and approach your neighbor. Politely tell them what's going on and attempt to resolve the issue like adults.

If that doesn't work, you move on to step two (which is what I had to do). Obtain a humane animal trap (my vet had one I was able to borrow for free) and trap the cat. Take it to the animal shelter and declare it a stray animal. They'll take it from there.

In my case, the neighbors didn't put a collar or any identification on the animal so there was really nothing to discern it from a stray/feral cat. They actually freaked out for two days before deciding to check the shelter, at which point they were able to retrieve their cat. I have not seen the cat since then.

But do not just trap the cat first, you must do the right thing and talk to your neighbor about the problem.

Good luck.