Step one, use the same account on your new android device,
If it does not get the license automatically, try to go to store, like David said, and click on restore purchase (left button on that picture, it's Grey if it works automatically, but if not you can click on that)
About the save file, it won't automatically transfer, you have to backup it manually at least once on your old device (new game/continue game => export and cloud save => export to cloud)
After that, as long as you use the same account, just import it the same way back, go to new game, click on export and cloud save and import from cloud.