Whether you have access to another user’s mailbox or a shared mailbox, if you are using Outlook 2010 or newer the mailbox will appear as a second mailbox in your folder pane automatically.
If you would like to access the other mailbox via Outlook Web Access, you will need to go to https://outlook.office365.com and log in to your account. Once you are in your mailbox, click on your picture in the upper right corner and select “Open another mailbox…” from the dropdown. Enter the email address for the mailbox and select Open. The additional mailbox will open in a new browser window.
If you are an administrator for your Office 365 account and need to grant a user access to an additional mailbox, you can find instructions here.