When a user is granted email delegation, you have access to read, manage, and send as on behalf of the user. This is required sometimes when accessing an email from a former employee.
This is a quick guide on how to open another mailbox in Outlook (assuming you have already requested delegation for the mailbox)
Option One - Outlook Client (computer based application)
1) Open Outlook
2) Click on the File tab at the top and then select Open & Export
3) From here, choose the Other User's Folder option
4) Enter the email address of the mailbox you want to open
Option Two - Outlook Web Client (Accessing Outlook via the Web)
1) Open your browser and go to outlook.office.com
2) Log in with your email address and computer password
3) Once you have your mailbox open, click on your image in the top right
4) From here you will see an option called Open another mailbox. Select this and enter the email address you need access to
5) Mailbox will open in a new page