The fact that Spain never formally renounced sovereignty is irrelevant – when Britain asserted its territorial claim Spain acquiesced.  Additionally if Spain’s claim did not lapse when it evacuated its colony then surely neither did Britain’s. Nor is it obvious that Argentina should have inherited the Spanish claim to the Falklands – they lie 250 miles off the coast of mainland South America.  Britain was of course not going to immediately contest the 1816 claim as she did not yet recognise Argentina so far as Britain was concern the Argentines were not sovereign and did not have sovereignty over any of their territory – at the time the UK recognised Spanish sovereignty over the mainland that Argentina claimed.