Let's say you want to send an email from email@example.com to firstname.lastname@example.org, where email@example.com is an account on your Postfix Dovecot email server. Hotmail is going to need some way of determining the IP address of example.com. You will need to configure your domain name MX (mail) records to point to the public IP address being used by your Postfix Dovecot email server. For example, in this image, example.com public IP address is 22.214.171.124, and the MX record then points to mail.example.com.
http://mxtoolbox.com can be used to verify that your MX record configuration is working properly on the Internet.
Open port 25 (SMTP) and port 587 (SMTPs) in your router and firewalls, and ensure your router is configured to point SMTP / SMTPs traffic to the privte IP address of your Postfix Dovecot email server.
You can now send a test email from firstname.lastname@example.org to email@example.com, and the email should be delivered to firstname.lastname@example.org.