What you need to do is to make the dog legally yours. You cannot determine that the dog has been abandoned, and you need to get - in writing - that they are transferring ownership of the dog to you. Get it signed at a notary if possible. Also have them call the vet and put YOUR name on the vet records. If the dog is microchipped, they will need to transfer the registry of the chip to you. At that point the dog is legally your dog, and you can rehome as you see fit. Your only other option, frankly, is to take the dogs to a shelter and have them contact the owners. You can then offer to take the dog to foster and find a home for. Note that you can take the dog to *any* shelter, not just the one where she was found.