As I understand it your JAA IR isn't valid in an N-reg a/c in the USA but they will give you an FAA IR on your FAA temp certificate providing you first pass either the FAA written (computer) IR exam or the IR (foreign pilot) computer exam. I assume the latter computer exam is just as subset of the former computer exam.
I should add that I have not done this myself so I stand to be corrected by anyone who has already gone down this road.