To give yourself or another user full access to someone else’s mailbox in Office 365 you have to use powershell. It can’t be done online.
In this example we are going to give Pieter full access to the mailbox of Danielle use this command:
Add-MailboxPermission Danielle@kops-ict.nl -User Pieter@kops-ict.nl -AccessRights FullAccess
As an alternative you can also give permissions to an inbox only
Here’s the code:
Add-MailboxFolderPermission -Identity Danielle@kops-ict.nl:\Inbox -User Pieter@kops-ict.nl -AccessRights Owner
For more detailed information, please refer below article:
Give an Administrator the Ability to Open and View the Contents of a User’s Mailbox(http://help.outlook.com/en-us/140/gg709759.aspx )