Microsoft offers email services for various domain names such as:
In order to download full contents of your mailbox, here are the steps you need to follow:
Download and install Download Mailbox Emails software for Windows.
Use the following information on the application:
IMAP Server: imap-mail.outlook.com
Server Port: 993
TLS: Implicit TLS
Click "Connect" button.
Then, choose INBOX (or any other folder).
Finally, click "Start Download" button. The contents of your INBOX will be downloaded (as EML files) into the specified directory.