Capt Airprox
Current means that it is current at the time of application for the Pilot Certificate. A licence can be current without being valid! i.e. the basic licence is within its validity period but the ratings in it may not be valid.
FAR 61.19 says the foreign licence must be "effective" not sure if that translates to current or valid in all respects. Even an expired licence can be effective for swatting flies!