Why is this needed?
Simple, Outlook, webmail, and Windows 8 app do not let you copy your emails from one service to another.Microsoft provides a service to copy emails from Gmail to Outlook.com if you use their default domains (@gmail.com and @outlook.com for example); but not if you use custom domain names (@yourdomain.com).
Before you get started
I am assuming that you have already set up your email custom domain in Outlook.com and have access to both email accounts. I may throw another article together soon for how to get started with your personal domain on Outlook.com.