I'm having the same problem. I have it checked as "Allow user to change password" but it's not working.
BTW, I have 4 security settings all of which allow password change. The only one that works is Full Access security.
FMP/S password change only works for FMP internal accounts.
External authentication is done through the OS. FMP/S cannot access the external authentication server so it cannot change passwords. Also, it wouldn't have admin privileges to do so anyway.