Both of them still claim it. It's still a pretty hot topic down there, the Argentines still believe that the islands are still rightfully theirs. I went to a Falkland Island museum in Rio Gallegos and the lady gave us a big speech on why they are technically still theirs (one of which is a land mass which extends from the mainland to the islands underwater). I'm not real sure on the whole thing, but from what I know, Argentina lost the war, so I would imagine that England has claim, but oh well.