There is absolutely no information anywhere that would legitimately support this par-baked conspiracy theory. The war was fought, Argentina lost and the British have had garrisons there ever since to protect their land. While recent treaties and resource sharing have softened the stance of these two nations toward each other, this area is indisputably a British possession.
There is absolutely no credible evidence that the United Kingdom would abandon the Falkland Islands and its residents to be occupied or annexed to Argentina. If so, it would be an even bigger betrayal by the UK than when it allowed Germany to occupy Czechoslovakia. It would be unthinkable and massive violation of the Islander's rights.