The Spanish never occupied the Falklands and they have never belonged to the Argentine (Argentina). The dispute about ownership of the Falklands is all about three things. OIL, GAS & FISH. All three are worth billions.
Let me explain a bit of the history.
The Falkland Islands have been occupied by the British as both a whaling station and for sheep farming for many generations.
Falkland Islands Oil and Gas Limited
http://www.fogl.com/fogl/en/home
http://www.iii.co.uk/investment/detail%3Fcode%3Dcotn:FOGL.L%26it%3Dle
Stanley airport is no longer just an air strip with a few battered huts. It can now take 747 Jumbo Jets.
http://www.youtube.com/watch?v=4DwWjAwZ118
The British have spent a lot of money in the Falklands, bringing the Islands into the 21stC. The Falklands now get about 91,000 visitors a year, some by sea others by air.
The Falkland Islands Company is a very profitable enterprise, now having more than just sheep and penguins to work with - it also has a booming deep fishing business and the tourist trade too. And, if you want to go somewhere wild, then head for the Falklands.
http://www.falklands.gov.fk/Trout_Fishing.html
Now let's go back to the time of the Falklands War and then step back about 100 years earlier than that to about the late 1870s. The Falklands were then under investigation by the Argentine for possibly taking possession, even though there were British citizens living there and working there, doing fishing and sheep farming and the then whaling industry.
The United States sent the warship, USS Lexington to Falklands waters and destroyed the Argentine Navy.
Although in the present age (21stC) the Americans are not going to say anything much, it should be clearly understood that the USA has an investment in the Falklands and that concerns any oil - which even at this early stage is estimated to be equal to Q8 in terms of barrels per etc.
But don't all rush at once. . .it's early days yet. The revenue from the Falklands will boost the UK economy big time.
On the question of nearness. Actually the Channel Islands are nearer to France than they are to UK - there is no dispute about ownership. But should oil be discovered off Jersey, there might be.
Take it from this expert screen watcher, the Argentinians want the oil and that's all there is to it.
They have no legal claim to the islands and never occupied them either as Spanish or later as the Argentine.
My advice to them - take a running jump - get lost.
There is a British Garrison of some 1,000 troops at/near Stanley including Gurkha's. Also a squadron of RAF Tornadoes etc.
http://www.youtube.com/watch?v=yuj05L_jbGo&feature=related