The thing is I can't see any reason Argentina "deserves" the Falklands, or even the surrounding waters.
Planting 3,000 colonists on an island nowhere near Great Britain doesn't in any way mean Great Britain ''deserves'' the Falklands either.
Argentinians deserve the Falklands the same way we'd reject France controlling Long Island. They don't want the British Empire in their back yard, claiming rights over the waters in that area. They've had enough of empires bossing them around.
We'll give it back when the American Empire gives Japan the Marianas and Cuba Guantanamo.