Thank you @ZhangHuangbin.
I have already set up a mail relay with Postfix on mydomain.com.
All mail sent from this server connects (SMTP) to my iRedMail-server to send out e-mails.
The relay is configured to connect/auth to mx.mailserver.com (iRedMail) with email user postmaster@mydomain.com.
However, mydomain.com have multiple system user accounts (each hosting various applications), e-mail is sent from mydomain.com with user1@mydomain.com, user2@mydomain.com, root@mydomain.com etc. as their FROM: address.
The web applications where SMTP is possible, like WordPress, is not a problem. However, all e-mails that WordPress sends out needs to be FROM: a valid user on mx.mailserver.com or it will be rejected as well. This stops me from using FROM: no-reply@mydomain.com on certain e-mails.
The immediate solution I can see is to allow postmaster@mydomain.com to send e-mails as any@mydomain.com. Please correct me if there is a better way.
Thank you.