Since I cannot link to a couple of British books on the subject that are out of print you may want to look at the history part of the following link..
http://en.wikipedia.org/wiki/Falkland_Islands
England claimed sovereignty in 1690, and has maintained their sovereignty.
Argentina wasn’t even an independent nation until the 19th century.
The Falkland Islands belong to the Brits, the people who live and vote there, and they don’t speak Spanish!