Earlier quoted context omitted.
In google play the purchaser information is mostly privatized and hidden from the developer. I assume Amazon is the same. The only way a developer would know a person is an existing user is if they have a user sign up process inside the app itself.
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
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.