Why? You don't need this.  As long as all tabs are using the same 
session, they will have the same key.

And this isn't going to work properly anyway.  To prevent session 
hijacking, we periodically regenerate the session ID.  This will work 
in one tab.  All other tabs will have session failures (since their 
session ID information is now expired).

You need to be using cookies if you want to be using more than one 
window and share a session.

Hello
Our users have access to individual mailboxes and to shared mailboxes.
Inside one web navigator instance, we would like to display several 
mailboxes (each in a separate tabulation). We used this kind of design 
with Horde 3.

We have 'no cookie session'.
The limitation seems to be linked with the 'horde_secret_key' cookie.

We found a workaround for enabling this feature:
in php/Horde/Session.php, function clean(), comment the ->setKey()

         $this->_start();
         // ** $GLOBALS['injector']->getInstance('Horde_Secret')->setKey();
         $this->_cleansession = true;
So all the opened mailboxes will share a common secret_key.

Thanks for your advises about this feature and this workaround.
Regards
Patrick