The 3,000 Falkland Islanders have the right to self determination under the UN charter.
Argentine politicians will use the 'Great Malvinas Lie' over the comming months as their economy takes a downturn and the Peso will probably be devalued. Much of Argentina's current economic problems are due to economic mismanagement. The country has more trade disputes running than any other country in the World and is the World's top protectionist country. Argentina is also regarded as a pariah state by international money lenders. All of this will take its toll on the Argentine economy.
The Argentine claims to the Falklands go back to 1833 after the Royal Navy removed a small Argentine garrison from the Falklands; Britain having already claimed the Falklands. In 1850 Argentina and Britain signed a treaty called the 'Convention of Settlement'. In the treaty both countries acknowledged that 'a state of perfect harmony had been restored.' and 'that neither country had any outstanding differences.' Later Argentine politicians acknowledged that this was the end to their claims to the Falklands and the Argentine governments in the 1870s and 1880s even produced maps that either omitted the Falklands from its territory or showed the Falklands in a different colour, like the '1882 Latzina Map' - successfully used by Chile in their 1970s Beagle Island Dispute with Argentina. The current claims to the Falklands made by Argentine politcians were started as late as the 1940s by the Peron government.
The Argentine claim to the Falklands is no stronger than Canada claiming Alaska because it's closer. Nevertheless, Argentine politicians will use the 'Great Malvinas Lie' to stir up nationalist feelings and to try and halt flagging ratings in the opinion polls.