[eluser]WanWizard[/eluser]
It is not possible to reuse the same session. Sessions are linked to an encrypted random session ID, that is stored in a cookie. Cookies are browser specific.
You could code your app so that information that needs to be shared isn't stored in the session record, but in the user record, and make some kind of remember me function that automatically logs the user in. You can store that in a separate cookie with it's own expiration.