Do you believe that people who take a homeless person's dog is in the right to give it away to a Pet shelter

Oddly specific scenario:

You're homeless , because rent just went up and its hard to find a place, you pack your stuff in your already paid off car, and you take your dog with you. You literally comb the streets for garbage so you can recycle it to get a meal for both you and your dog. The dog gets immunized, is fed nearly daily.

One day, you're out picking trash while walking your dog, and someone sees the dog, asks to pet it and then the moment you're not looking, snatches the dog and gives it to a local pet shelter.

Is the person who stole the dog entitled to give your dog away to a pet shelter?

Or is the person who stole the dog not in the right, and should be charged with petty theft.