Great to see that someone else on this forum thinks the Falkland Islands is a good place to start an AU project!
I have two variants of a Falkland Islands AU in development on this forum;
1: a version that is still largely a dependency of Great Britain but develops its own military capacities in the years surrounding the 1982 Argentine Invasion that allow some interesting 'what-ifs' to be explored. And;
2: a full blown AU nation of considerable economic and military power that gains independence as a Commonwealth Dominion in the 1890s and plays a substantial role in the geopolitical events of the 20th Century. This Au nation encompasses a significant portion of the South American land mass, in addition to the falklands themselves.
Check out the following links to threads i've already got in the works.
Look forward to seeing what you come up with!
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DCFI (Falkland Islands) AU Nation