They don't need their nuclear weapons to be deployed stationary anywhere near the Falklands since they have ballistic-missile submarines which can deliver a nuclear warhead right to the coast of Argentina itself (or elsewhere, for that matter). You should be well familiar with the accident which happened in February 2009 when two submarines collided in the Atlantic ocean
One of them was British nuclear-powered ballistic missile submarine HMS Vanguard
Some nations also have disguised secret underground missile bases.
The united states was known to have one buried beneath the ice sheet in greenland, under project iceworm.
https://en.wikipedia.org/wiki/Project_Iceworm