If I understand correctly you now have your media in a folder A1 which is not the media folder for your tree A1B1 and FTM knows where all this media is located.
Can I suggest you try the following (make sure you have full backups first). Go to the media manager n A1B1 select all the media, (which is linked to A1), and then in the media menu select copy media. FTM will ask you if you want to copy the media into the media folder, to which the answer is yes. I have done this with a small number of files (108) and it works and is quick. You may have to split your 16,000 into more manageable blocks but this is way quicker than allowing FTM to search for missing media.