Question

How to resend those messages by scripts that were rejected by outgoing mail control?

Answer

If a message was blocked by the outgoing mail control, it does not get queued or saved, it just gets rejected (dropped) without the ability to resend it. This is done to prevent spamming on a server.

If a regular mail user tried to send a message when the limit of outgoing messages was exceeded, a notification would appear that it's not possible to send email now. In this case, the message does not go anywhere: the page just stays on the "Write New Email" step. For details about how outgoing mail control works, visit Plesk Administrator Guide.