The Falklands were never inhabited by aboriginals.
Yep. That was one of reasons of Argentina’s objections to the British claim, that the british citizens are not indigenous to the island.
In fact, there is no evidence that Aboriginal or Argentinian people had ever visited or had knowledge that the islands existed prior to the British arriving.
That’s not true. Check out the wiki page about it, it has a whole timeline, including who lived on it when.
Also, Argentina claims ownership by inheritance from Spain when they won their independence from Spain.