I would suggest contact with the CAA before moving on. They are hidebound.
Check with the new FTO if they can fit their curriculum around what you have already done. Reason? The CAA are hidebound. They agree a curriculum with FTOs but don't check if you have fulfilled all the exercises unless you go to another FTO - you, the candidate, are the one who will suffer for any shortfall of your previous to latter change. Like an MOT, FTOs are given the annual blessing one day in the year - they can generally do what they like for the next 364/5.
If you can possibly avoid changing, then do that.