You may normally have access to other Outlook mailboxes, but they are not immediately visible in the online/web version of Outlook. To open another mailbox, first click your portrait at the top right of the screen:
You will see the option to open another mailbox. Click this, then start typing the name or email address of the mailbox you want to open. A list of options will start to appear; when you see the mailbox you're looking for, click on it, then click Open.
You will now be able to see and respond to emails coming to this address.