Chabad is providing an answer to all animal lovers:
I adopted a feral cat this January and I am quite happy with her. Jerry is outside most of the day and in the evening she comes in in order to eat and sleep. She loves laying on my bed and stretching out. Making me only a guest on my bed. 🙂
Last November, I had taken in a feral male cat called Sparky by he died in an accident shortly after. Thus I know how hard it is to lose a pet. I was crying out my eyes for about a week.
On the other hand I have to admit that I am going with the Ramak (Rabbi Moshe Cordovero) stating that the animal’s soul is returning to it’s original place and does not continue to exist. But there is, of course, no definite answer because nobody knows for sure. The Ramak’s statement seems logical and this is why I go with it.