Using android.content.SharedPreferences, set one singaling the user purchased a license from the Amazon copy of the app, read it from the Google Play app.
It is doable, the main issues is: 1. Getting users to redownload the app from the Play store 2. Maintaining this registration transfer mechanism
I think issue #1 is a big one, how to download a paid app without paying for it? Not everything is freemium.
Shattered Pixel Dungeon was a good example of me paying on one platform, and then applying the upgrade to the free app after downloading on another.