I wasn't exactly a supporter of Thatcher - we are still suffering from many of the social changes she inflicted on us, and she jumped at the chance of a war to bolster her popularity, which is ironic as that is exactly why the Galtieri regeime invaded the Falklands.
With regards to who has the legitimate claim to the islands, Argentina have geographical proximity on their side but little else. Britain's claim is by long term settlement (oddly, not always a strong case - ask the Palestinians), and it should be noted that the inhabitants were not full British citizens at the time - they are now. The UK and Argentina were feeling their way towards negotiations regarding shared sovereignty, which the Argentines effectively scuppered by invading.
I very much doubt that Britain would ever enter into such negotiations now, and that is the Argentinians own fault. The bottom line is that it has to be down to the inhabitants to decide, and they are pretty unanimously pro-Britain.