Pilotchute, unfortunately the FSDO is correct. The DPE/ADP/inspector that issued your ATP would have had to issue the A320 type rating at that time and certified that you completed the type rating course under part 142 (or part 121 or 135 where applicable). If you did not do a part 142 course for the type rating, and only did a course for the ATP, despite the fact that you did it in an A320 simulator, you cannot have the A320 type rating added. The FAA does not convert type ratings and you need to do the full course and have it certified as such.