the falklanders will never use AA, they`ll use LAN because they offer a reliable and good service for years now, they are cheaper and LAN is part of a huge airline alliance connecting destinations all around the world.
Some Falklanders/visitors might use AA for a flight from Bs As, because they could connect in EZE with a direct flight from LHR. It would involve a 2 leg flight instead of the current 5-6 leg flight and save at least 8 hours of flight time (my calculation) which would be appealing. Still, I'll believe it if it ever happens.