Take a look in the folder /Videos/FBX Game Recorder/Recordings. You should be able to find the original MP4 recording file there.
To add the original again to the FBX recordings list:
Make a copy of the original MP4 file in Windows
In the Recordings tab, go to the top of the list and click the '+' button to the left of the Date - Game tabs.
Select the MP4 file copy you just made