A complement to this guide:
http://www.angrybirdsnest.com/angry-birds-ultimate-backup-tutorial-for-all-platforms/
Usual disclaimer: You follow this guide at your own risk and I accept no responsibility for damage you may do to your phone because it. That said, the procedure for WP 8.1 requires no permanent change to your phone and should be far less risky than the procedure for Win 10 (which requires what some call jailbreaking the phone). Thus, if at all possible, you should transfer scores from an 8.1 phone to an 8.1 phone and then upgrade the OS to Win 10. Even, revert a phone from 10 to 8.1, if possible, before beginning this operation.
I have no procedure for Windows Phone 8.0 and earlier. Some of the precursor tools to what are used in the Windows 10 Mobile procedure may be of help if you really need to go down that road.
Windows Phone 8.1
(Scroll halfway down this page for Windows 10 Mobile [⚡️] instructions.)
NOTE: You must “developer unlock” your phone to install the tools needed to gain access to the encrypted part of the SD card (D:\WPSystem) where the files of interest are stored. Developer unlocking is a standard, Microsoft-built procedure. This is a bit laborious but possibly not as bad as what one must do to an Android 😉.
Name That Tech 