My data totally justify my conclusion, Jake. They make it clear that the islands have NEVER "belonged" to Argentina in any sense of that word. If they now "belong" to Tierra del Fuego province, 1861 is the earliest possible date that any Argentinian claim can be valid. We'd been there for a century plus by that time.
Apart from the "Bagsies I saw it first international law," what OTHER international law was there regarding discovered territory in the 17th/18th centuries? When some intrepid skipper set foot upon an alien shore, he generally planted a national flag and said, "This land is now British/Portuguese/Dutch" or whatever. That's why, for example, Australians speak English (after a fashion) and Brazilians speak Portuguese.
In 1982, the Argentinians tried planting THEIR flag on the Falklands, but it didn't fly for very long and - for as long as the inhabitants there remain largely British - I trust it never will.