Moral dilemma

Need a sounding board. I'm sure y'all will have an opinion. Hopefully this won't get too heated. Here's the issue...

There is a house one street over from ours that has a mutt that is constantly roaming the neighborhood taunting all the other dogs. He comes and stands at our fence at 3am and makes Tate bark like a mad man. I'm not talking 1 time a month, I'm talking 1-5 nights a week! I've even yelled at the owner before and told him to keep his dog on a leash/in his yard or I'll call animal control (not really) after another sleepless night. It's obvious that these people don't give a c@#$ about their dog. He 'get's out'. Um, yeah, 5 nights a week? Anyways...it happened again last night, and after watching the animal control van circle the block all day (I didn't call them!), I decided to catch him. I did and he's in our house right now, happy as can be. Here's the problem. I don't see the point in returning him. They don't want to take care of him and when animal control picks him up, he'll inevitably be euthanized. I want to take him to a no-kill shelter and let him find a better home.

My only issue is that it's kinda stealing, but I really want to put the poor dog's best interests first. If this was a child roaming the streets 5 nights a week, there'd be no way it'd go home again.

What would you do?