You could take the cat to a shelter or a cat rescue, letting them know you found a stray and that you yourself want to adopt the cat after a period of time.

 I also protected & cared for some Thai Wild Crocs in the nearby Mangrove swamp, & a very large Python; plus numerous smaller snakes, birds, mice & Scorpions. 'Pythagoras' as I called him, was wild, huge & always came to see me when I walked in his territory. I roughly measured him at around five meters, about 16 feet, weighed around 80 Kg or 175 pounds. Thankfully he genuinely was 'friendly', since he was big enough to hurt me, or take any of the dogs I walked with. Python lived just behind my home, could easily have come in, but kept to himself. So far as I am concerned all life is Sentient; though of course, the level of sophistication varies. But every creature I ever encountered had a personality, habits & responded to kindness; or even simply company. I'm not sure where you are, but if it is the US then I'm shocked to hear of strays. Forgive me please, I'm an old Brit who used to a different kind if normal. Anyway, good luck with the dogs; you can Train them, but it takes time. It may be simpler to 'train/educate' the passers-by?

You have a couple of options here. First, you could take the cat to a shelter or a cat rescue, letting them know you found a stray and that you yourself want to adopt the cat after a period of time. I would bet good money your neighbor will not be interested enough to check the shelters when his cat goes missing. After a while, the cat becomes available, you adopt it, all is well. Second, you could just spirit the animal away into your household. It would have to be an indoor cat, obviously. I doubt your neighbor will ask if you have seen it, but get ready to be a good liar, just in case. Whatever you do, act soon. I waited to adopt a feral cat that I had finally tamed. I called him Mr. Lau. He was a beautiful tuxedo cat. I already have 4 cats so I told myself I couldn’t take him. The last time I saw him, he looked thin and sick. He was still friendly and ate heartily. But I never saw him again after that and I am fairly sure he died. Had I gotten him vet care, he might be alive. It broke my heart.

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