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If you already have postfix properly set up and running, edit /etc/postfix/main.cf and append this:

smtp_sasl_auth_enable = yes
relayhost = smtp.mailgun.org
smtp_sasl_security_options = noanonymous
smtp_sasl_password_maps = hash:/etc/postfix/sasl_passwd

Then add your smtp credential of mailgun to postfix:

echo 'smtp.mailgun.org username@domain.com:password' > /etc/postfix/sasl_passwd

Protect the file and populate it:

chmod 600 /etc/postfix/sasl_passwd
postmap /etc/postfix/sasl_passwd

And finally restart postfix:

service postfix restart

Now your server should send its mails via mailgun. Just give it a test shot!