Almost all of the population of the Falkland Islands lives on East Falkland, with about 80% of the population living in the capital, Port Stanley. A small number (less than 200, I think) live on the other large island, West Falkland. I am not aware of any of the other islands being permanently inhabited.
The total population of the islands is less than 3,500. When you consider that number of people arrive in the UK by rubber boat most weeks when the weather is decent, you can see it is a non-starter to think of sending them there (not that the Falklands' government would put up with it anyway).