Users logged out - wrong encryption of password in cookie

I think, there's a little mistake in the code:

setcookie($cookie_prefix .'password', md5(md5($vbuser['password']) . $vbuser['salt']), $expire, $cookie_path, $cookie_domain);

This is the way passwords are stored in the database. So you take the already encrypted password in the database and encrypt it with salt and md5 again. But the password in cookies is encrypted this way:

setcookie($cookie_prefix .'password', md5($vbuser['password'] . '*YOUR LICENCE NUMBER*'), $expire, $cookie_path, $cookie_domain);

(of course you have to replace *YOUR LICENCE NUMBER* with your vBulletin licence number).

After replacing this part, everything works fine and the users are not logged out at the end of the session lifetime.
I used Drupal 5.7 and vBulletin 3.7.1 Patch Level 2