I had the same problem. This is because the code actually uses what email ID you set under General > Settings in dashboard. Some servers do not allow you to send mails from other servers. (I use bluehost and I had to go to my host and make sure the email is registered in cpanel) So this is what I did:
Edited the “new-user-approve.php”
– Changed the line:
$admin_email = get_option( 'admin_email' );
to
$admin_email = '[email protected]';
Hope it temporarily solves the issue!