Actually the first colonists were French. The claim was transferred to Spain via a pact between the Bourbon kings of both countries. The Spanish name for The Falklands derives from the French, Îles Malouines, named after Saint-Malo/Sant-Maloù.
The Argentinians only ever occupied the islands for six months, for a penal colony - which ended via mutiny, not military expulsion. They've otherwise been under continuous British occupation since 1833, barring the 1982 war.
I'm English, and by no means pro-English colonialism, but the Argentine claim is spurious nonsense.
At least twice