An FAA IR can use his (her) rating on a G reg aircraft only in the UK, but on an N reg anywhere?
No, not quite. The privileges of an FAA IR can be exercised on a G-reg aircraft, but not for IFR flight in controlled airspace. In principle this should apply in any state's airspace, but it might be worth checking that the state in question honours the CAA's (automatic) validation of the FAA licence before relying on it. Many states have no real concept of IFR outside controlled airspace, so it may not be of much use outside the UK.
As IO540 notes, the CAA will issue an IMC rating on a JAA licence on the strength of a FAA/IR as a paperwork-only exercise. This would extend the privilege above in effect to allow IFR flight in classes D and E.