Even though the overwhelming opinion here is that the Falklands and it's dependencies are British, I still feel I need to add my voice to the crowd.
Argentina is in part basing it's claim off the backs of the Spanish, in truth the Falklands have been British and occupied by Brits since before Argentina even existed, so right there your claim is baseless.
To the person who said that before the sheep the Falklands were covered in trees, that I would like to see, having been there and seen nothing above a bush on the islands I find it hard to believe trees were ever there, maybe a lot of bushes an penguins but no real trees.
As to the simple person who said we would never have won if the US hadn't helped, sorry Mack but the only thing we got from the good ol US of A during this conflict was outdated satellite info and some Sidewinder missiles (that came at a hefty price), which we used to shoot down US supplied A4's and French supplied Super Etendards.
Having been to these islands I can tell you the inhabitants DO NOT want to be Argentine, only to be left alone and determine their own destiny.
To the honorary US/RN Matelot yep we still have beer and spirits (For Senior Rates and Officers), onboard pussers grey war canoes and I have more than a few good stories, so pull up a bollard the dit spinning is about to begin.