Here are the steps to forward a mailbox in Office 365 to another users mailbox.  This step will often be done when a user is terminated or leaves the company along with converting the mailbox to a shared mailbox to preserve a license.

Forward a User Mailbox in Office 365:

  1. Go to the O365 Exchange Admin Center: https://outlook.office365.com/ecp/
  2. Browse to recipients and on the mailboxes tab click the magnifying glass to search for the users mailbox you want to forward.
  3. Double click on the user to edit the properties for the mailbox.
  4. Select mailbox features and scroll down to Mail Flow and click View details.
  5. Check the Enable forwarding box.
  6. Browse and select the users mailbox you wish to forward this mailbox to.  Note: you can choose to check the box ‘Deliver message to both forwarding address and mailbox’ if desired.
  7. Select OK and Save to complete the mailbox forwarding.