Argentina had been sabre rattling in the south Atlantic for a number of years. In 1977? The Labour government had sent a small naval force to deter any Argentinian threat.
Thatcher and the Conservative government could never have expected the Argentines to invade. The Defence review of 1981 would have removed the Navy's capability to retake the islands and if Argentina had waited a few more months then this would have been the case.
The most compelling case that would be utilised against the accusation of the BG lying and orchestrating an invasion is the conflict itself.
When the surrender came, the British Task Force was within 10 days of logistical failure, the Navy had taken heavy casulaties in ships and the Army was in danger of grinding to a complete halt. Had one of the two carriers been hit or sunk, then unless Illustrious or the crippled Bulwark could be hurriedly sent from the UK then a stalemate, perhaps even a British defeat was on the cards. Combine this with the the danger of the exocet missile and many other factors, then the chances of conspiracy are minimal.
In conclusion, the war did wonders for Thatcher, Britains standing in the world and put the Great back into Great Britain.
'We have ceased to be a nation in retreat' Margaret Thatcher July 1982.
A far more interesting discussion would be on the Belgrano.