In Outlook on the Web (OWA) the shared mailboxes you have access to do not automatically appear under your primary mailbox like they do in the desktop client. Follow those instructions to open a shared mailbox in OWA:

Add the shared mailbox under your primary mailbox:

1. Sign in to OWA with your work Microsoft account (read how to sign in here)
2. Right-click Folders and select Add shared folder
3. Start typing the email address of the shared mailbox and select it when it appears, then click Add

If you want to receive notifications for the shared mailbox, then you need to open the mailbox in a separate window. See instructions below.

Open a shared mailbox in a separate window:

1. In Outlook on the Web, click on your profile in the top right corner
2. Select Open another mailbox
3. Start typing the email address of the shared mailbox in the search field and select it when it appears
4. Click Open