So SRSLY, this is how I'd take Islas Malvinas ...
STEP 1: fire a volley of Argentina's new PCX missiles from the mainland toward the runway at Mount Pleasant, destroying the runway and confining the Eurofighters to the ground (unless they're already airborne, in which case the FAA will just have to wait a few hours for them to run out of fuel and fall out of the sky)
STEP 2: with air defenses neutered, drop a company of paratroopers on Port Howard (pop. 20) in the western islands where there are no British troops, secure the boat dock
STEP 3: calmly dock a Ro-Ro in Port Howard and unload three batteries of 155mm howitzers ... break for 2 hours to celebrate Carnival
STEP 4: send a cruise ship chartered by the Brazilian Red Cross to moor off the coast of Stanley ... telephone the British Governor and inform him the entire population of Stanley has 4 hours to get aboard it
STEP 5: after 4 hours, start popping off 100 high-explosive shells per hour at Stanley ... within 10 hours, 1000 shells will have hit the town, 2 for every building
STEP 6: land a company of sappers on the eastern and western islands, start randomly laying mines everywhere, with no rhyme or reason
STEP 7: send a press release to the Guardian ... let them know the islanders have all left by cruise ship and, if they return, the islands are now totally uninhabitable - every building has been destroyed and you can't walk 10 feet without stepping on a land mine
STEP 8: the islanders are now removed from the equation - the UK government has to mobilize their population for war only for oil rights, not with the excuse of defense of the kelpers since they're gone and will never be able to return ... the Argentine embassy in London can then start handing out fifty-quid notes to local chavs to have them wander around the streets for a few hours carrying "No Blood for Oil!" signs - Julian Assange can make a speech from the balcony of the Peruvian embassy
STEP 9: + 10 days later
maybe a British fleet of 12 ships shows up with no aircraft/aircraft carriers ... chugs around the islands shaking their fists at the Argentine troops from the decks of the UK's two Type 45 destroyers ... Argentine Navy stays safe and snugly moored in Buenos Aires ... New York Mercantile Exchange sets a date for opening bids in the auction of petroleum franchises in Argentine-controlled Islas Malvinas