I just found this on http://community.office365.com/en-us/forums/613/t/54315.aspx but wanted to re-produce it hear for safe keeping.

To allow another user to open additional mailboxes in O365 they need the relevant permission.

Open a powershell window and connect to your tenant with admin credentials.

This example command allows John to open Jerry’s mailbox:
Add-MailboxPermission [email protected] -User  [email protected] -AccessRights FullAccess

If you also want the 3rd part to be able to send as this user you need to also issue this command:

Add-RecipientPermission [email protected] -AccessRights SendAs -Trustee [email protected]