In modern times, people have a habit of getting over wars, particularly stupid ones. By the late 60's, JFK was getting a hero's welcome in Berlin, same for the Japanese and the US; by the 1990's the US and Vietnam had resumed full relations; etc. But not here, because of course not.
The Falklands War was about the stupidest a war could get. Britain was shedding colonies and territories by the dozen, the Falklanders did not have full British citizenship, and it was widely seen as a matter of time before the Falklands passed to Argentine control.
The war was started by a failing government, now widely reviled, in an attempt to shore up domestic support. They managed to fail even at this, even with the UK on the other side of the world and the US regarding a British victory as "militarily impossible". They literally snatched defeat from the jaws of victory.
It is highly ironic that the people who protest the most against that government, and never tire of tarring their purported successors with the "genocidal" and "Nazi" brush, seem to regard this absurd war as the one good thing they did. For the same reason, by the way: trying to score cheap political points, devoid of any substance.
No sentiment that the Falklands conflict was a ridiculous idea, poorly executed, which pretty much put the brakes on the Falkland being Argentine for at least a generation.
It would be more than difficult for the islands to be ceded to Argentina when the islanders quite definitely want to remain under British rule. And after a war was fought it just isn't going to happen.