I'm afraid there is no quick solution for this.
Acchieving the wanted behaviour would at least require heavy changes to several scripts and modifying your php configuration, so that the session-id is handled over automatically.
If you can't modify your php configuration, you'll have to append the session-id to every link. So you'll have to modify every single script.
Lot of work for a "little effort", i think.
Changing the login/authentication mechanism is more a question of basic software design. In most cases, it's a bad idea to hack that.
