This error drove me nuts!
I contacted the hosts, deactivated plugins etc etc
What finally worked was changing a line in /wp-includes/pluggable.php
// $phpmailer->setFrom( $from_email, $from_name );
$phpmailer->setFrom( “email@example.com”, $from_name, false );
I also created this email wordpress@[mywebsite.com] – so it is a real email account – not sure if that helped or not.
How I found a fix:
I started with this one – go down the bottoms & Pstenue links to another couple of pages and that’s where I found the answer.
It’s all working now – phew!
So now all I have to do is make sure all client site emails are sending from their own email address rather than the wordpress@ that I created.