I think there were no people at all in the Falklands before the British discovered it & Colonized it. That would make them the "indigenous people" eh?

Two others, Spain and (I forget) also set up colonies later, but didn't oust the Brits or claim the whole thing. Eventually there were conflicts and GB did claim the whole thing.

And yes, even shortly before the Argentinian invasion they had held a vote on it & a vast majority said to stay British.