I instructed the CAA and FAA courses in the USA (dual citizen). The loophole that allowed FAA to teach there is closing up. Just as the "students" that are actually working there are starting to close up by the FAA. There are many areas of part 61 which the EASA students do not demonstrate and thus should not be signed off for solo! But to teach the EASA ppl/cpl I had to do a course with the head of training in my ATO. I was then given a caa reference number which allowed me to teach various courses at the school. So in short you are standardised by the school.
FAA to EASA conversion (sorry it is a little long):
I have just converted my ATPL from FAA to EASA (FI info lower down the page), what I did was the following:
I hold an FAA ATP, which is in the UK described as a professional licence. I was therefore exempt from the ground school requirement. I did however have to take the 14 exams. Most of the exams easy, some are just of no use in practical terms whatsoever and are hard to study for because of that. If you have an ATP you just saved a few quid as you don't need a brush up course!
There are exemptions for the RT test, you would need to look at cap 804. But from memory if you have X international flight hours you don't need to do the RT test.
After you have done the exams you need a medical and some form of skills test. I did my skills test in a sim, it was an aircraft which I have 3000 or so hours in and was really very straight forward. No oral examination just the flight. But I could of taken the skills test in a different sim which I had no previous experience after a full training course.
Now I am doing the Flight instructor conversion. Which again there is a reduction for!
In the UK you have to do a pre course assessment to enable you to start the FI course. The CAA state that everyone has to do the 30hr ground and 15hr flight course BUT the ATO which you are doing it at can request a reduction in these times if you hold a valid ICAO flight instructors rating which you do as the FAA is ICAO.
Feel free to email me if you like if you want more info as I have just been through this and It wasn't easy