Summary
Open OWA as you usually would, click on the right-hand icon and select open another mailbox, you should then be able to access any mailbox you have access to.
Body
Navigate to https://outlook.office.com/ and sign in with your regular credentials
Accept the Duo Multi-Factor prompt
Select your icon in the top right hand corner, and then select Open another mailbox.
In the new pop up type the name of the departmental mailbox and select open.
