I know its stored within the folder /program files/AEBPlus because every time that I upgrade I just copy the entire folder back over over after installing the application. After that all my associations are back. Also first I run AEBPlusUnload.exe before copying the files back.
EDIT: They are stored in AEBPlus.cfg Just open that file with a text editor (
frNotepad) and you will be able to see your Activation Key and all of your settings.