I agree that the FI should remain British but God knows what will happen if & when memories fade or we hit a full scale crisis
If they can get the oil on stream they'll be able to make an increased "voluntary contribution" to keep the armed forces there (or hire others to protect them).
If I was Argentinean I'd play a very long game - restore flights, lift sanctions and the nit-picking and just treat the inhabitants reasonably (maybe add in freebees such as university education, subsidised travel etc). Realistically aim to replace the UK as the Governing Power in say 50 years but offer exactly the same degree of self-government