However, if Britain leaves the European Union without a deal, the islands' economy — heavily reliant on tariff-free squid exports to EU member Spain — could face a hammer blow.
Argentine Foreign Minister Jorge Faurie made waves last month, saying Buenos Aires would exploit Brexit to enhance its diplomatic push for the Falklands.
Britain's sovereignty claim to the islands dates back to 1765 and it has held permanent administration since 1833. Buenos Aires claims the barren, windswept islands, 400 kilometers from the Argentine coast, are occupied Argentine territory.
Argentina's then-ruling military junta invaded on April 2, 1982 but surrendered on June 14 to a British task force after a brief but intense and bloody war.
Faurie told AFP in New York in November that Buenos Aires was discussing with London the possibility of "creating more connectivity to the islands."
"There is a lot of room still to grow in terms of confidence and trust between the two countries," he said. "Our expectation is that the rebuilding of bilateral trust... will constitute a sort of substantive material to discuss all other issues about the sovereignty of the Malvinas."
Once Britain is outside the EU in March 2019, the 27 other states will no longer be obliged to support London's sovereignty position.
Brexit is also an opportune moment for Anglo-Argentine ties: Britain is seeking new trade partners outside the EU while Argentina needs to find ways out of an economic crisis.
"Post-Brexit, (Argentines) are imagining that if the Malvinas Islands has to get its economic act in order, that may open up channels," Richard Lapper, a South America specialist at Chatham House, the Royal Institute of International Affairs think-tank in London, told AFP.
"The big prize for Britain is the prospect of very cheap agricultural imports. The Argentines may say they only want to do a deal on food if we have a side agreement on the Falklands."
As an EU member state's overseas territory, the Malvinas Islands enjoy tariff- and quota-free access to the European single market. Some 94 percent of fisheries exports go to the EU, contributing 40 percent of the islands' GDP and a third of government revenue. The second-biggest sector is meat and wool exports.
It is estimated that a no-deal Brexit would shrink the Malvinas government's revenue by up to 16 percent, damaging its ability to deliver public services and invest in roads and hospitals.
Tariffs would "wipe out the EU as a market for meat exports", while there "really isn't an alternative market" for its squid than southern Europe, said Richard Hyslop, senior policy advisor to the Malvinas Islands government. "The fishing industry is a huge success story for the Malvinas and we don't want to see anything happen that damages that," he told AFP.
Even so, establishing alternative trade links with Argentina seems a long way off. Their sovereignty claim is enshrined in the constitution and Kirchner-era legislation aimed at frustrating the Malvinas economy remains in place.
"Certainly I don't think anyone's looking at direct trade with Argentina," said Teslyn Barkman, the Falklands lawmaker responsible for Brexit, the EU and natural resources. "Regardless of Brexit, they would be trying to find opportunities to work this sovereignty conversation into any development," she added.