If the UK has no claim to the Falklands, then who does? Remember that whilst the UK is a state in its own right, it is made up of several different countries. You could class the Falkland Islands as one of these countries inside the Union, in fact they are in some sense more autonomous than the other countries that make up the UK. The SNP are calling for independence in Scotland as they have every right to do, but the Falkland Islands aren't. Neither are the people in Bermuda, Gilbraltar, the Cayman Islands, Anguilla and all the other overseas territories that are part of the United Kingdom.
No land belongs rightfully to any entity, just because Argentina belives it should be part of Argentina, despite very little historical precedent to suggest that it should be, doesn't mean that the Falklands should be belong to them. We captured it through military conquest, and if Argentina wants it they'd have to do the same because they have no right to the islands - it's the way the world has worked since the dawn of man.
