The save files are stored in a separate folder from the game. If you're using Windows there should be a folder named Pokemon Rejuvenation in the Saved Games folder in your user account (C:\Users\your name\Saved Games\Pokemon Rejuvenation). This folder contains your progress and all the backup saves. Copy this folder into the Saved Games folder on your new computer, and then you can just download a new copy of the game and your save file will carry over.