To be part of Britain, like they always have been. Argentina never had a claim to those islands.
They were Spanish before Argentina’s independence (hence the Argentine claim); a British ship stopped there and planted a flag (hence the British claim).
That the people there want is irrelevant, because then the newcomer simply inundates it with settlers to claim they are answering a majority’s needs/desires. Happened in the north of Ireland, in Gibraltar, Morocco is doing it in Western Sahara, etc.
Actually, the Falklands can never be part of “Britain” because Great Britain is an island, not a country.