Technically the French were the first to inhabit the Islands closely followed by the British. The Spanish Empire did have a claim when the French handed their possession to them.
This is true, though it could be argued that Spain allways considered the islands Spanish, even if she didn't settled in them. That's why she reacted as she did when she found out of the British and the French settlements. The French agreed to abandon them peacefully. Great Britain didn't.
They even had settlements there at various times but independent Argentina has no historical claim on the islands.
This isn't exactly true. The British were expelled by the Spanish in 1770. The British threatened Spain to go to war, so they were allow to return. According to the Argentine version of history, this was just to save British honour: the British had secretly agreed with the Spanish to abandon the islands. This may be false, and it can be proved in either way anyways. But the facts are that Britain abandoned the islands in 1774, three years after they had returned.
Spain was there till 1811, when she abandoned the islands to defend Montevideo from the forces of Buenos Aires. Nobody else was there permanently from 1811 to 1829. Argentina declared her independence in 1816. It send a ship to claim the islands in 1820. This was based on the principle of
uti possedetis: the new countries were entilted to the land they possessed when they were colonies (
the Malvinas had always been under the control of the governor of Buenos Aires). This principle was applied in Latin America to delimit the new states in early XIX century, and would be applied in Africa more than a century later, after decolonisation.
Great Britain recognised the independence of Argentina in 1825, without saying anything about the islands. Argentina founded a settlement in 1829. The British took it by force in 1833 (almost 50 years after the last time they had been there), sending its inhabitants back to Argentina.
I don't want to turn this thread into a discussion about the legitimacy of Argentina's claim, but I just wanted to explain you why I disagree with the part of your post in which you said that "independent Argentina has no historical claim on the islands"