This article explains how to access a shared mailbox using Web Outlook. 

After you have accessed the shared mailbox you might also want to look at the article How to send an e-mail from a shared mailbox, to make sure that your e-mail is sent from the shared mailbox address 

Login to your Office 365 account
Click on Outlook to open it and access your e-mails
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In the left hand Navigation Pane, right-click on Folders

Click Add shared folder

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Type the name or e-mail address of the shared mailbox in the Add Shared Folder dialog box.

From the list of shared mailboxes suggested, click on the one that you wish to open. In this example School Events

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Click Add to add the shared folder to your Outlook shared mailbox 04
You will now see your chosen Shared mailbox added under the default 'Folders' entry shared mailbox 05
Click on the chevron (>) to expand the shared folder shared mailbox 06

The shared mailbox will expand and show you the various folders associated with it, for example the inbox.

You can now access and use this shared mailbox from within your Outlook

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