I challenge you to tell us exactly which one(s) of these schools train for FAA and then do a conversion test....or retract the statement.
None that I am aware of....I meant some US schools. I am making the point that SOME schools in the USA bypass CAA approval by the methods I suggest.
The skills test for a "conversion" does not have to be done at an approved place, nor the IMCr test either, which is how SOME places can do JAA / CAA ratings with no approval.
One thing you have to be careful of though is being ripped off by JAA schools in the USA. I have known SOME schools to charge UK or nearly UK prices for essentially FAA training, followed by a JAA examiner's flight test. I even went to one CAA approved place, and they charged one rate for an FAA person renting the aeroplane and one for the JAA person !!!!! The same plane, the same reg etc.....They use it to milk unsuspecting Europeans of their hard earned cash.
My advice would be to forget JAA and do an FAA PPL which is perfectly usable in the UK without formality - no conversion required.....