Condolences on your loss.
The spirit of Rex is forever attached to your spirit. The past is not non-existent. It’s still space and all its contents in other time frames. In those time frame you are both still there.
When your time of passing comes you’ll be taking Rex with you through the Door. It’s a very hard time of waiting and separation. Crushing times apart. Grabbing another 4-legged friend for eternity is the best relief.