by Rosario Carcò.
Sorry for being late. But we solved such SINGLE SIGN on for Web-Applications nation-wide here in Switzerland using Shibboleth (see www.switch.ch/aai). And fortunately Moodle supports natively shibboleth authentication. So your two web-systems should simply support shibboleth auth and the web-browser would transparently allow logon on both web-applications.
Rosario