I've followed this thread for a week or so and have resisted the temptation to get stuck into this; but on a damp Sunday afternoon between paperwork, the temptation is overwhelming. And full marks to Cosmicomet and maddog37 for continuing to make their points - but gentlemen, here's why it's doomed- my apologies for not having enough Spanish to write it in your mother tongue. In advance, my apologies for the length.
<<International Law Anorak Mode: ON>>
It is widely accepted that the islands never had an aboriginal population, so before their discovery in 1600 (ironically, by Seebald de Weert, a Dutchman), they were unknown to humans. Initially called the Sebald Islands, they were named the Falklands by the British in 1690 after John Strong named them after Viscount Falkland, Commissioner of the Admiralty. However, there was no permanent settlement on the islands - variously claimed by Britain, France, Holland and Spain - until the French arrived in 1764, establishing Port Louis on Berkeley Sound, East Falkland (north of Stanley). Port Louis was sold to Spain in 1767.
Meanwhile, the Brits were busy establishing a colony at Port Egmont, on Byron Sound - West Falkland. It is probable that the British and French / Spanish didn't know that the others were even there - Byron Sound is on the northern coast of West Falkland and everyone concerned seems to have believed that they had been banished to some godforsaken windswept wilderness on the edge of the world; at least both sides had this in common.
When they found out about Port Egmont, the Spanish were enraged, and attacked the place twice before the British surrendered and sailed on 10 June 1770 under protest. This eviction nearly precipitated war between Britain and Spain in Europe as well as the South Atlantic, with a deal done to allow the British to return - which they did in 1771 before departing again in 1774, but not without leaving a lead plaque which claimed the whole archipelago for Britain forever.
In 1790, an agreement called the Nootka Sound Accords was signed, which didn't help matters at all by talking about "the adjacent islands" to the South American mainland - without telling us whether this covered the Falklands or not. By 1811, the Spainish governor also ordered the Spanish colony to withdraw from the islands.
So, when the United Provinces of Rio de la Plata - that would become Argentina - revolted against the Spanish in 1816 and gained independence, it took seven years to emplace another colony on the islands, achieved in 1823. For the next 10 years, Argentina occupied the islands, despite the British claim from nearly 60 years earlier, before Britain returned under Captain John Onslow to Port Egmont, West Falkland in 1832, and forcing the surrender and evacuation of Puerto de la Soledad on 4 Jan 1833. The Union Flag would fly over Stanley until 1982.
Thus, though a legal argument can be made about the legal status down to 1833, it is quicker, easier (and probably more accurate) to accept that the British takeover in 1833 was imperial conquest. Which as this was the principal mode of territorial acquisition in 1833 - and had been for 5000 years - should excite no-one.
So what happened in the 149 years of British rule? Firstly, the UN Charter was adopted in 1945 and the UN would lead on decolonisation based on self-determination. However, as the Falkland Islanders had become the indigenous population since 1833, their wishes were the ones which need to be observed - not those of the Argentine settlers expelled more than a century before.
Hence, the fundamental problem for Argentina: if you accept self-determination as the cornerstone of international sovereignty, then you'll have to wait for the Islanders to decide to become Argentines. If Argentina doesn't accept self-determination as the basis, then they should say so, and be howled down by the rest of the international community who do accept it.
Alternatively, Argentina could invade again, but as acquisition of territory by conquest has been illegal since 1945, they'd also have to bin the UN Charter as well.
<<International Law Anorak Mode: OFF>>
Bottom line: the islanders will determine the future status of the islands - be that British, Argentine or independent. Good luck to them!
S41