No.
The Falkland Islands are owned by the United Kingdom.
Argentina however believes the UK should give the islands to them, however.
In 1982, Argentina invaded the Falklands Islands - in doing so, they automatically declared war on the United Kingdom.
The UK, USA and UN condemned the actions of Argentina and demanded their withdrawal from the islands. Argentina refused, so the UK were forced to liberate the Falkland Islands through military force.
The USA, although they didn't attack Argentina, did patrol the oceans around the islands, because they were worried that Argentina would run to the Soviet Union for aid against the UK.
France supported the UK by sending technical teams and engineers with the British Royal Navy - although France did not officially declare war on Argentina.
Recently, in 2012 onwards, Argentina have shown increased aggression again, surrounding the islands. The UK now has naval warships patrolling the oceans around Argentina and have built a new permanent Royal Air Force base on the islands - ready to defend against another potential invasion. Next time, the UK may take the fight into Argentina itself, to teach them to back off.
Falkland Islands, South Georgia---Islands off South America, owned by U.K.
The group of islands, located 300miles from South America's Patagonian coast is called Falkland Islands. They are one of the British overseas territories and not part of South America.
The continent of South America is the nearest to the Falkland Islands, and the country of Argentina is the closest country. The Falklands are part of the United Kingdom although they are claimed by Argentina, which calls them the Isla Malvinas.
They are part of the British Overseas Territory
Galapagos
Some of these major islands are the Malvinas or Falkland Islands claimed by Argentina and Britain and the Galapagos Island that is a part of Ecuador. Juan Fernandez Islands and Easter Island are territories of Chile. All these countries are in South America.
The southernmost tip of South America is part of Chile.
South America The Falkland Current is a cold ocean current that flows along the southeast coast of South America.
Tierra del Fuego, the lowest part of South America, is an island formed by the Strait of Magellan. However, it is part of Argentina and Chile.Islands to the east in the South Atlantic include the Falkland Islands (Malvinas), site of a 1982 war between the UK and Argentina. Other islands are the frigid South Georgia Islands and the South Sandwich Islands, all under the administration of the United Kingdom.
South America
Part of falkland islands
The largest non-independent area is French Guiana, formerly a colony and now an overseas territory of France. The Falkland Islands, as well as other islands off the coast of Argentina, are territories of the UK.