If your Microsoft 365 mailbox is one of several mailboxes you need to check, it's possible to set up an automatic forward to an external or primary email address using Inbox Rules.
Rules allow you to move, flag, and respond to email messages automatically. You can also use rules to play sounds, move messages to folders, or display new item alerts.
Rules can be set within Outlook on your desktop device (both macOS and PC) or through the Outlook Web App. The example here shows how to create a forwarding rule within the Outlook Web App.
1. Sign in to Outlook online via office.com.
2. Click on the gear icon in the top right hand corner and choose View all Outlook settings at the bottom of the side menu.
3. Choose the Mail option in the left sidebar of the popup dialogue box, select Rules from the adjacent list of options and click on Add new rule.
4. Create a rule similar to the example shown below.
It's possible to extend basic rules and automatically file messages into specific folders depending on how you want to manage your inbox.
Setting Rules in Desktop Versions of Outlook
The process for setting rules in the desktop version of Outlook is similar to the above with the same options available. Once you've set these, they'll automatically be applied to server and work irrespective of whether Outlook is open or not.