At last, what a mission!
I sourced some code that gave me access to the detail I needed from the Service Provider (of cause they could have given it to me). I saved the following code in a file called test.php
<?php phpinfo() ?>
And then viewed the file in a normal browser. This gave me access to all the server settings. From there I changed 3 things:
1. Entered the correct Server Name.
2. Entered the correct Port number.
3. Replaced the From Email Address with a false email address.
I think number three was the most important, as the clients email address was a different domain name. So I made up an email address that ended in the same domain as the website address did. And it worked!
Thanks again for your assistance.