The Falklands government keeps a separate civil aviation department. Their charts are not in the list provided in the above link. The ICAO code you are looking for is SFAL.
Here's some information on Port Stanley's airport:http://en.wikipedia.org/wiki/Port_Stanley_Airport
Good luck finding those charts. I've tried to obtain them too, but last time I checked, their civil aviation handler lacks a published AIP (an online accesible one, anyways).
If you really, REALLY want them, you could always contact the issuing authority.
Here's some contact info I found on them:
Falkland Islands Government
Civil Aviation Department
Falkland Islands, FIQQ 1ZZ
Tel: + 500 27300
Fax: + 500 27302
P.S. If you do find them... Share! ;D