License verification is handled by the Google Play Store.
Please make sure you are signed in to the Google account connected to the purchase on the device and download AccuBattery using this same Google account you paid with.
License verification can also fail if Google Play Store and/or Google Play Services is disabled so please make sure they're enabled. If you are in a country where the Play Store is blocked (for example China) then that could also explain why your license is not working.
Make sure that you don't have anything like Lucky Patcher installed.
Restarting your phone can sometimes help as well. When the license is active it will be possible to see this under settings > 'my purchases'.
*If you used a backup/restore app to reinstall AccuBattery that can also lead to issues, please try reinstalling from the Play Store. (This will reset your AccuBattery settings and history!)
Another thing to try is to clear the app data of the Play Store app itself via phone settings > apps > all apps > Play Store > clear data.
If it still doesn't work please send us an email at firstname.lastname@example.org with the Google email address you used to make the purchase and mention that you've tried the above steps already (or if you skipped a particular one). Also include either your order number (usually starts with GPA...) or let me know approximately when you bought the app). Thanks in advance.