That’s a pack of lies. A British colony at Egmont existed before Spain ever enteredt thee picture. The French established a small private colony despite previous Portuguese, English, and Dutch claims of discovery. The British shortly afterwards established their own colony while being unaware the private French colony had been established nearby a few years previously. The French sold whatever rights they did or did not possess to the Spanish. The Spanish claimed the islands by right of conquest when they drove the British colonists out of the Falklands, but this nearly led to war. Spain settled the dispute and allowed the British coony to be reestablished. The Spanish recognition of the British colony thereby negated later claims of an exclusive sovereignty in the Falklands. Spain withdrew its colony and Britain withdrew its colony again, while retaining their respective claims to sovereignty over the Falklands. A predecessor government, the United Provinces of the Platte, attempted to pirate away the prior claims of Britain and Spain, but they never succeeded in stablishing a legitimate government in the Falklands, and no Argentine goverment ever established any settlement or colony in the Falklands. Instead, the Falklands were under the control of pirates from the evacuation of the British and French-Spanish colonies until the reestablishment of the British settlements. The only nations to have ever established settlements in competing claims for sovereignty were France, Britain, and Spain. Argentina never inherited any Spanish claims, because the Spanish cclaim was lost after Argentina had already come into existence and would have been in conflict with the prior exercise of sovereignty by Spain. Spain subsequently recognized British sovereignty in the Falklands, so Argentina has no lawful basis to claim a right already abandoned or settled by treaty by Spain.
Argentina has no rightful claim to the Falklands by any theory of inheritance or possession. Furthermore, Argentina is in violation of the Charter of the United Nations waging a war of aggression upon Britain. If Argentina makes any further war upon the Falklands, its government should be treated like that of NAZI Germany.
I could get an Argentine to give me the same story in reverse. In any case, asking British residents transplanted there means nothing; it has the same validity as asking the Scottish transplants to northern Ireland.