I found the following (and slightly amusing) extract in Harris's thrilling read 'Cases and Materials on International Law'5 Edn 1998 p 214:
19. The Argentine Government formally protested against Britain's occupation of the Islands in 1833, 1834, 1841, 1842, and 1849, in the latter year sending a note to the British Government indicating that, although not intending to protest any further in view of Britain's inattention to her protests, Argentine silence should not be interpreted as aquiescence. [In other words, Britain gave Argentina a stiff ignoring until 1955, when as a result of claims agaisnt other South Atlantic Dependencies...]...Britain sought in 1955 to institute proceedings at the International Court of Justice [The Hague] both against Argentina and Chille concerning their respective claims to sovereignty over the Falkand Island Dependencies and British Antarctic Territory, but neither the Argentine nor the Chilean governments agrees to accept the jurisdiction of the Court...[probably because the outcome was clear - the titles would be formally ceded to Britain].
And finally, from Akehurst (1983):
A State, in order to acquire title to territory from another State by prescription, must exercise effective control over that territory for a long period The UK has clearly satisfied this requirement...[which should be] accompanied by acquiescence by the 'losing State.
Argentina has claimed that it has protested over the years, but apart from the invasion in 1982 [an action against international law], Argentina has never sought arbitration or taken further diplomatic steps, such as breaking off diplomatic relations with Britain. Moreover, within the doctrine of intertemporal law, conquest establishing title in 1833 is accepted as legitimate.
So, let Argentina take it to arbitration (not bilateral taklks) and see how, err, succesful they might be in gaining the Islands back, lawfully this time.