EASA IR -> PIGGY BACK FAA IR

To jonas: yep, you are right, that's how I understand it

Jonas, you are correct, there is no requirement to demonstrate your IFR skills, you already did that by virtue of having an ICAO IFR License. As you stated, you must be current, but this is not an issue with adding the IFR privilege to your US Private Pilot Certificate issued on the basis of your ICAO License. Since you are current per 61.56 and 61.57, once you have your US IFR added to your certificate, technically you are legal to fly. I am sure that any rental agency will require a checkout and some might have restrictions for using their aircraft under IFR, but that is a commercial matter and not a legal one.