Argentina (ruled at the time by a failing military dictatorship) lost any legitimate claim it may have had to the islands after it invaded in 1982. They gambled that Britain didn't have the means or the will to do anything about it...and lost.
The irony is that the British government really didn't have much interest in the islands (few British people knew what or where they were); had Argentina been more patient, by now the islands would almost certainly be called Malvinas. But aggression cannot, must not and will not go unanswered.
Argentina, you had your chance and you blew it. But if you really, really, really want the islands, you could try offering Her Majesty's Government £1trillion cash and half of any oil produced and 10% of any oil revenues you accrue and full relocation costs for any islanders who don't want to become Argentinian. No? I thought not.