Figures. If you download the app again, it'll be a new space. Of course the game would restart from the beginning. You've made an in-app purchase means you have an account for it to apply to, all you gotta do after installing the app is to log in by your account that had already made a purchase. That's why I asked you if you have linked your game account to FB so wherever device (and virtual space or emulators) you play the game, you can always reload your save from FB.