Here are untested ideas (may be not working) on how to workaround blocked e-mails by the server provider / datacenter /

Exim reject log can return following error or other errors indicating e-mail was not delivered:

"You do not have sufficient privileges to send mail to this address. Please authenticate and try again."

One can try to setup MX DNS entry, send FROM e-mail address that exist and that can accept e-mail (verify it). In case of WHM/cPanel, make sure in WHM / Exim Configuration Manager / Basic configuration the option "Reject remote mail sent to the server's hostname" is not enabled.

Other more difficult workarounds (untested, unsure if would work):

- Setup scripts to find php mail and a) contact users with tutorial on how to fix or b) fix it somehow for them
- How to relay all e-mail outside of current server and send from outside? (google: mailserver send proxy OR relay OR forward)
- Buy new server and migrate accounts
- Setup GRE tunnel as a proxy to server (google: buyvm gre tunnel)?
- change port used by mail transfer agent (exim for example) from 25 to something else?
- Relay mail via remote server:
- Disable mail() function