I saw on my loop (but did not read) an Islamic attack on Israel claiming they "armed Argentina". Trying to get Brits onside in an anti Israel post.
Truth is, if any country can sell its arms they will to almost any buyer. The US must sell a whole lot of kit to Argentina, as does Israel (and possibly us?). It's just trade.
Take the 1982 conflict. By far our closest and most loyal ally in the conflict was France (certainly not the - at best - ambivalent Americans who were happily supporting an awful despotic Junta). Yet we were being pounded by French made Mirage jets and Exocet missiles.
It's not a secret what the US did anymore and you are incorrect. I am able to tell you.
MI6 had to have intelligence officers selling fake exocets to undermine French sales - in France. Unfortunately, even without live warheads, the fuel propulsion system burned out ships.
The US actually gave over it's GPS system ( early day Motorola satellites) so that the UK had locked in coordinates of forces - friend and foe. There was very little artillery.
How did it do so much accurate support?
They had to do it secretly due to US/ Argentina relations. They became economically entwined afterwards. However that went.
The US also relayed what Chile was reading on its radar. When planes took off in Argentina, Britain was getting warning. Didn't always work - the bombers always get through. If you're willing to lose enough.
Then there was Ascension. It was previously a British base. When it was used for refueling and resupply it was nearly entirely a US base. We can argue about the fall of the empire but it remains that the US sanctioned that resupply.
The main issue with the Falklands was little more than Government cuts. If British armed forces had been much better equipped there would have been far less casualties. The main thing is how good the soldiers/ sailors/ Airmen were. That was what won it.