Englishgal's point - here's a weird one - the medical must be valid for the original licence - so UK licence UK medical - if the JAR standard (or what ever alphabetti spaghetti) Class 2 medical cannot be passed but the FAA Class 3 can, one simply can't just go get an FAA Class 3 and use that - the key is that the originating licence must be valid so if JAR have a current Class 2 medical and a JAR flight review in addition to the US one.
In those circumstances I do wonder if one can do a stand-alone FAA PPL get a Class 3 FAA medical and piggy-back a JAR - I assume there is some sort of reciprocal arrangement - no idea if there is - any one know the current rules on this issue (they do seem to change all the time)?
How does an FAA PPL holder legally fly in UK/EASA/JAR land?