To keep the new-posting-notification-function active even if the admin change some user-details in the usermanagement-panel, you have to change a few more lines.

Again includes/admin.inc.php on line 138, change the "0" info a "1". The line finally should look like this:

if(isset($_POST['new_posting_notification'])) $new_posting_notification = trim($_POST['new_posting_notification']); else $new_posting_notification = 1;

To avoid the new-posting-notification is set to "0" when a user edit his profile, you have to change the file includes/unser.inc.php at line 472. You have to change again the "0" into a "1". The line finally should look like this:

if(isset($_POST['new_posting_notification']) && $_SESSION[$settings['session_prefix'].'user_type']>0) $new_posting_notification = intval($_POST['new_posting_notification']);
else $new_posting_notification = 1;

and i moreover change the line 481 (don't know it is really necessary). It finaly look like this:

$new_posting_notification = 1;

Good luck