that may lawfully be kept may be given away by its owner, because giving it amounts in reality to relinquishing his exclusive right to that dog.

But if someone keeps a dog in a situation in which it is not permissible to keep one, then gives it away, this is not valid. For the person giving away this dog has no right to it, since he is not permitted to keep it in the first place. So how can he relinquish something to which he has no right?!