”I believe that the islanders should have control of the islands.
If they want to continue as a British Overseas Territory then I have no objection to that. If they wish instead to ally themselves to the closer Argentina, then, again, that is up to them.”

That’s one solution which, on the face of it, sounds very reasonable, and I’d agree with you if the Islanders were a genuine indigenous population. But they are not - they are comparatively recent settlers and descendants of settlers and, in the main, they are British - no prize for guessing which of those two they would almost certainly choose!

I think that, in view of the fact that both the U.K. and Argentina have strong, legitimate claims to the Falklands/Las Malvinas archipelago, it would be a matter better settled by the International Court of Justice.