Lovely. The History of the Falkland Islands (which is riddled with arguments for various countries involved in the disputes and does not neutrally present the facts of the history) leads one to the 1833 invasion article, which is a biased misnomer in the first place since Aregentina had invaded and did not have a recognised claim on the islands (in fact, their claim had just been disputed by the United States who had bombarded the city after removing its entire population of German citizens from Argentina.

The Argentinians then decided to make the islands a penal colony, and sent a miltary group there to set it up. But the soldiers and prisoners mutinied and killed their chief officer in November. Another officer was dispatched who settled the mutiny and restored order, but in January was confronted with a superior force of the British Navy who ordered him to depart. Which he did.

Beyond this I can find extensive speculation but no factual support, especially for various myths regarding Antonio Rivero.