I think I may have a solution to this one.....
From what I can gather, Argentina is desperate to own a windswept lump of rock, miles from nowhere, devoid of civilisation and with nothing to do other than spot sheep (yes I did say "spot").
Said lump of rock needs to have its own airfield, and maybe a smaller one thrown in........ so in return for abandoning their claim on the Falklands, let's offer them Anglesey! It'll save the taxpayer the cost of maintaining a garrison 8,000 miles from the UK and the even higher cost of subsidising the armpit of the universe.