I have the free version of the 'My Boy!' GBA emulator for Android. If I were to get the full version would I still be able to carry the saved game files from the free version to the full version? I'm using a Galaxy S4 if that makes a difference.
Your current (GBA Battery) saves will work in the premium version. Based on the site's FAQ, the saves are located in a the root folder of the ROM:
In-game save files are named as XXXX.sav, in the same directory as the game file is in.
This means that if your ROM is on "/storage/sdcard0/games", then the .sav (which is the battery save) would be in that same folder.
Note: The .SAV files that have been created may not work properly with any other emulator. As long as it's made by the same team, then your saves will appear like normal.