A little history first. From what I can make out...more or less...
Pre 1522 the islands may or may not have been reached by Pategonian Indians
1522-1600 sighted by Portuguese, British and Dutch ships; may or may not have been overwintered in by the Spanish
1690 Britain explored them
1764 France inhabited the east
1765 Britain inhabited the west
1766 Spain compensated France to abandon the east
1767 Spain expelled Britain but later returned the west
1774 Britain departed but left plaque claiming sovereignty
1811 Spain evacuated
1820 Argentina set up a colony
1831 USA proclaimed the islands free of all government
1832 Argentina set up a new government
1833 Britain expelled Argentina
1965 UN Resolution 2065 asserted the Falklands/Malvinas constitute a colony and called on Britain and Argentina to negotiate taking account of the islanders interests
I think the islanders have made it plain on several occasions they want to remain under British rule.
However, it has been said the islanders' views don't count because they are an implanted population, starting in 1833.
Hmm...how long do you have to be somewhere before your views count? It's been 180 years since the implantation started in 1833. Perhaps the occupants of the USA weren't entitled to declare independence in 1776; after all, it had only been 211 years since the first permanent European settlement in 1565!
The majority of British residents could be on dodgy ground too. Britian has been invaded by the Normans, Vikings, Jutes, Saxons, Angles, Celts and Romans. Perhaps there are some Neanderthals out there who'd like to register a prior claim?
Argentina itself started as a colony in 1536 and didn't become independent of Spain until 1861. Now, who lived in Argentina before 1536...?