As Saphroneth has pointed out, there's essentially only a few outcomes.
Bare in mind, though, the UK has a history of continuing to fight when faced with a serious defeat - a failure to retake the Falklands in itself while a defeat, wouldn't be the end - accepting Argentina's victory, though, would be. The UK is very unlikely to go for this.
As such, what does the UK have left?
HMS Invincible
HMS Hermes
Both of those fought in the Falklands.
HMS Illustrious - she arrived about 3 weeks after the war ended. She's definitely available.
HMS Ark Royal - she was launched and entering her "fitting out" stage in 1981. Commissioned in 1985 historically - so its entirely possible she could have been brought into service in 1983 if the UK goes all out.
HMS Bulwark - HMS Hermes sister, she entered mothball in March 1981 due to a fire she had sustained while conducting a exercise, she wasn't in great condition, but she was actually announced to bring back into service at the beginning of the Falklands War - however, her fire damage was extensive so she wasn't. A prolonged conflict though, with the UK pushed back from the Falklands in 1982 and forced to try again in the spring/summer or 1983?
She ll almost certainly be reactivated - that gives the Royal Navy all winter & the start of 1983 to get her back into fighting condition - alongside fitting out HMS Ark Royal.
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Basically, a UK counter-attack in 1983 see's Argentina, in the very best case scenario, facing down 3 Royal Navy Aircraft Carriers (HMS Illustrious, HMS Hermes & HMS Invincible).
More likely? It runs the very real risk of the UK sending all 5 against Argentina (HMS Illustrious, HMS Hermes, HMS Invincible, HMS Ark Royal, HMS Bulwark).
It also gives the UK all winter to recall her escorts back home, resupply them & conduct any minor repairs to ensure they are all in peak-condition, while also arranging with allies (i.e. Australia, New Zealand, Canada etc...) for them to stand in for UK RN deployment-commitments, like some of them historically did.
That means the RN's surface fleet could be substantially larger than the 1982 Taskforce. Combine this with a better organised & prepared Amphibious & Auxiliary force.... then things become EXTREMELY dicey for Argentina.
Lets not forget: Historically the RN, while sustaining losses to Argentinian Air attacks, ripped the guts out of the Argentinian Airforce in the process - its why the Royal Navy won., the RN could sustain the losses & attrition: The Argentinian Airforce, couldn't.
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Basically, there is no easy "Argentina Wins" button here - they might, if they play their cards right, manage to beat the 1982 Taskforce back, but beyond that? Unless the UK gives up (& generally, it doesn't give up when directly threatened by another nation, let alone when its territory is invaded and citizens occupied at gun point), 1983 see's a massive effort by the RN and likely a much more bloody & intense war, which almost certainly ends in a UK victory with a substantial risk of the conflict escalating beyond the Falklands (I.e. the UK targeting the mainland, Argentinian Navy etc... etc...)