I am very sorry to say that, as our son found out the hard way,
if you give up a pet to a Pet Rescue organization, there is a very great
likelihood that they will not allow the pet to be re-adopted by the same person after the pet has recovered. He found a Border collie, which he had wanted all his life, advertised in the newspaper as "free to a good home." It turned out that the dog was very listless and, when examined at the vet's, was discovered to have the worst case of heartworms they had ever seen.
Our son did not have the large amount of money to pay for the treatment,
which would in all likelihood have killed the dog. His only course was to give the dog up to Border Collie Rescue, since they could arrange for the dog's treatment. He was very disappointed that, after she recovered, he was not allowed to re-adopt her. I can see their point, since they have no way of knowing that he was trying to help her and wasn't the uncaring owner who had allowed her to get in that condition in the first place. This is something that people need to be aware of before taking this step. I know that this discussion was from several years ago, but new readers might benefit from reading this.