When receiving email in Outlook or similar email program it shows "on behalf of" for the email address FROM line. This is standard procedure on emails here at Total Server Solutions if you send emails from one address, but define the FROM field as a different address.
To stop this from showing or to resolve this you will need to create an email address in cPanel that actually has the real FROM address defined. The SENDER email address and the FROM email address must be the same in order to avoid the notice in the email headers.
Why do Total Server Solutions employ the usage of the "on behalf of" noctice? The main reason is Spam. Nobody likes spam. For years, spammers would spoof email headers to say that mail was being sent from one address when it was really coming from another. This helps cut out any fake emails and makes it easy for our staff to track who was the real sender. This also provides legit information to the end user to tell them that yes, the email address really does exist.
So to fix, just be sure whatever email address you're sending from actually exists in cPanel, and this will resolve the issue.
If you are using a VPS or Dedicated Server and wish to disable the notification of the "on behalf of", you can disable the checkbox in the Exim Configuration Editor for the following entry:
Set the Sender: Header when the mail sender changes the sender (-f flag passed to sendmail).
Be aware that this will make your spam tracking much more difficult.