PN, I think that the furthest you could go is to call the ownership of the islands "disputed"; the Americans opt for this description
"Falkland Islands (Islas Malvinas) (overseas territory of the UK; also claimed by Argentina)"
(See:
https://www.cia.gov/library/publicat...k/geos/fk.html)
The legal case would be immeasurably strengthened if there was a free and fair referendum of the inhabitants on the future of the territory. Of course Argentina will refuse to recognise the result, and claim (improbably) that if you were going to have a referendum, you'd need to include the great-great-great-great (etc etc) grandchildren of the Argentine settlers who were booted off in 1833-34 (though not all were).
But the beauty of this is would be to settle once and for the next wee while questions of popular will amongst the islanders, which does matter in the legal and political realms.
And there probably will be another war over the islands, but only if the UK denudes them of meaningful protection.
AFAIK, the Argentine forces are in an even more parlous state than the UK forces. So it should be a while yet - and in the meantime, let's hope the Int boys and girls provide the necessary warning for reinforcement.
S41