In Office 365 you can open another user’s mailbox. Here’s how.
Go to the outlook web access page. In the left column find your username and right click on it.
Then select “Other user’s inbox”
In the dialog box that appears, enter the name of the desired mailbox or use the addressbook icon to do a full search.
And click OK. Now you will see the other user’s mailbox appear in the left column.
When you receive an error stating that you have no permission to open the inbox when you are sure it exists, you may need to get the right permissions from your administrator.
I also have an article that explains how to set the right permissions.
Read it here.