Althought the transient_id option is active, the session_id is lost
after using the header() method in order to redirect to another
script.

You're right, the session id is not added when doing redirects. You have
to do it 'manually', with something 
like this:

header("Location: $url.'?$PHPSESSID'");

Reclassified as documentation problem.
Note: IIRC there's also feature/change request about this.

--Jani

I've tried the recommended solution==>
 header("Location:$url.'?$PHPSESSID'");

This fails for me.

My example:
 $SID1=$SID // * up at the top
 Header ("Location:registration.php.'?$SID1'");
Notice the strange registration.php. in the middle.  Well php doesn't
like it either.

Any other recommendations?

oops..my example was buggy..it should be something like this:

header("Location: $someurl".'?'.session_name().'='.session_id());

This bug has been fixed in the documentation's XML sources. Since the
online and downloadable versions of the documentation need some time
to get updated, we would like to ask you to be a bit patient.

Thank you for the report, and for helping us make our documentation
better.

"Session ID is not passed with Location header even if
session.use_trans_sid is enabled. It must by passed manually using SID 
constant."