You need to get your history straight. He didn't help. In fact, the Reagan Administratrion opposed Thatcher's invasion of the Falklands. See:
http://reason.com/blog/2010/02/26/obamas-falklands-neutrality-po
(And I remember all too well how disappointed many of us Reagan supporters were at the time.)
Is that why Reagan fired Al Haig for supporting Argentina? Is that why he sent an emergency shipment of AIM9s to Ascension Island?
Reagan would have preferred that the matter be settled peacefully and tried to facilitate a negotiated settlement. At the time Argentina was providing trainers and logistic support for El Salvador in their war against the communists and Reagan wanted to retain that support if at all possible. The US did not support the sinking of the Belgrano (Phoenix) but then there was criticism of that action in the UK as well. When it became apparent that there was going to be no peaceful solution to the conflict and it came down to supporting an important NATO ally over a non-aligned dictatorship. Reagan made the right decisions.