British sovereignty dates back to 1765 but the first reliable sighting of the Islands are by the Dutch in 1600; in 1690 Captain John Strong on the Welfare discovered the channel between the Islands. But unfortunately the first 1764 settlement was by the French Navigator/Military Commander Louis Antoine de Bougainville in present day Port Louis East Falkland, in 1765 Captain John Byron claimed West Falklands with the first British settlement in 1766, so really it is a Hodge poge of claims on the Islands between the Dutch French and British.
You really have to wonder Argentine objectives and how far they could go in their efforts to claim the Falklands in a current article in the Navy magazine (printed by the Navy League of Australia) Argentina has withdrawn cooperation in the South Atlantic Fisheries Commission and extended its fishing seasons which will have a long term impact on fish stocks for the Falkland Islanders, rejected the 1995 joint declaration on Hydrocarbons in cooperation agreement between Argentina and the Falklands and placing a ban on charter flights travelling thru Argentine airspace to the Islands in 2003.
But if the British government as announced some time ago that they which to reengage with Australia/New Zealand in the long term not only in a military sense but an economic sense. From a fibre optic security view, plans exit that might make it feasible to lay a cable from Australia to New Zealand to the Falklands Island then onto south America then into Europe to safe guard our cables that currently run through north and potential conflict zones, not only then would the UK have a vested interest in the security of the Falklands but also Australia and New Zealand which new Zealand did provide assistance to the British task force in 1982 by replacing a Frigate in the Indian Ocean. With increased co-operation between the MOD, NZDF and ADF and future goodwill visits by the RNZN and RAN might pressure the Argentines from the aggressive talk and mitigate any thought of an adventuress engagement against the Falklands in the future.