Representatives of the Argentinian government were invited, including the ambassador, but chose to turn it down. The prime minister would not have been invited, as it was not (technically) a formal state funeral.

As for the obssession with the Falklands, it was an important conflict. It was the last war that Britain fought alone in terms of actual fighting: we had some logistical and intelligence support from France, who were insturmental in shutting down Argentina's supply of Exocet missiles, and the USA and Chile provided some radar and satellite information, but it was the last time British forces fought a conflict alone. It also demonstrated a willingness to defend sovereign British territory which has informed British discussions with other countries over issues such as Gibraltar and Northern Ireland. It also demonstrated the value of new technology (the Harrier). It was also a war we did not want to fight against an enemy we did not particularly dislike (Britain and Argentina, this issue aside, usually have good relations) and which resulted in 900-odd deaths to no avail. That still rankles.