FAA license outside of USA
 

Let's assume the pilot with FAA ATPL license works in airline operator that is registered in country "A" ( ICAO member). However, all aircrafts in that company registered in another country "B".
So, aviation regulations in country A state that each crewmember have to get a validation from country B ( 83bis agreement)

Questions are:
How can the pilot comply with airman currency requirements? Do i need to be current according to FAA rules(part 121 or 135)? Or regular line checks, FFS sim checks conducted by airline are accepted?

I know a couple of such examples. I just confused what regulations must i comply with.

P.S. Country A doesn't have any license conversion process from FAA or EASA to it's national ATPL.

Norwegian Air?

Nope! But there is no difference. Any thoughts on the subject?

To my knowledge in order to fly commercially and to be the legal PIC of the aircraft the pilot must hold the respective license in accordance with the aircraft's registration (e.g. N-registered aircraft = FAA license, or EASA license = EASA registered aircraft) or hold both licenses and thus, has to comply with the respective (or both) currency requirements. If an airline operates aircraft (and crew) of foreign registration they must comply with the respective regulations and currency requirements. But since most countries are ICAO members anyway (except the country of West-Sahara and a few remote islands in the pacific) pilot licenses are issued in accordance with ICAO Annex 01 FCL (Flight Crew Licensing) and the currency requirements are pretty much similar (e.g. 3 T/O and landings within the proceeding 90 days and 6 approaches within 6 month or 3 app. within 3 months which amounts to the same anyway).