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Allow user to send email without smtp authentication

Create a plain text file: /etc/postfix/accepted_unauth_senders, list all users' email addresses which are allowed to send email without smtp authentication. We use user email address user@example.com for example:

user@example.com OK

Create hash db file with postmap command:

# postmap hash:/etc/postfix/accepted_unauth_senders

Modify Postfix config file /etc/postfix/main.cf to use this text file:

smtpd_sender_restrictions = 
    check_sender_access hash:/etc/postfix/accepted_unauth_senders,
    [...OTHER RESTRICTIONS HERE...]

Restart/reload postfix to make it work:

# /etc/init.d/postfix restart