How to access https page via wget or curl?
The problem is not the SSL / https. The problem is the fact that facebook sees "wget" as the agent and tells "update your browser".
You have to fool facebook with the --user-agent switch and imitate a modern browser.
wget --user-agent="Mozilla/5.0 (Windows NT 5.2; rv:2.0.1) Gecko/20100101 Firefox/4.0.1" https://facebook.com/USERNAME -O index.html
and then you will see the actual facebook page if you open index.html in a modern browser.