If Argentina had been smart the following could have happened:
1 - Argentina seeks closer ties with the UK via trade and invites the Falklands Islands to join an economic union using it as a great commerce resource for accessing Uk and European markets. The British love trade.
2 - Argentina asks to share defensive responsibilities with the Uk in a treaty ; sharing the Falklands bases and developing them for large aircraft and deep hull ports. The UK - glad of an ally - shares operations. Argentina - a responsible member of the international community proves its worth over decades working closely with the Royal Navy and relieving the British of an expensive but tactically vital role.
3 - Argentina draws up a treaty recognising the rights of the Falklanders to self determination and offers a standing invitation - should they ever wish it - to be part of Argentina but ensuring that everyone is aware that they will fiercely respect their rights to remain British or whatever they so wish.
4 - Oil is discovered and Argentina immediately opens up tax breaks to its ally's oil companies. Oil refineries are built on Argentinian soil including a pipeline costing billions. Argentina gets access to international oil expertise and billions of yearly revenues from oil refining.
5 Argentina gains access to very cheap oil.
6 Britain and Argentina forge a great friendship based upon mutual trust and shared common concerns. Potentially the Falklanders may one day choose to join Argentina especially since many of their burgeoning population (driven by trade and oil industries) are Argentinian and are great friends. Britain ,no longer a colonial power, is at the forefront of granting people self determination and democracy and will not stand in the way of any of it's former territories choices.
Compare and contrast what Argentina has achieved so far and is doing now because they are too greedy. The Argentinian administration are pillocks concerning this matter. imo.