If the string always starts with http://www.fam.com/FAM# then it's simple: that's 23 characters, so take the substring from position 23 (note that indices are zero-based).
String input = "http://www.fam.com/FAM#Bruno12/06/2011";
String result = input.substring(23);
If you want everything after the first # in the string, then search for # and take everything that comes after it:
int index = input.indexOf('#');
String result = input.substring(index + 1);
(error checking omitted for simplicity).
To remove the date, remove the last 10 characters.
See the API documentation of class String for useful methods.