Full Access Permissions
You may want to give user's permissions over a particular mailbox. This can be done through the Hosted Services Control Panel.
Note: This will give the user you add Full Access to a mailbox, they will be able to access the other mailbox in its entirety.
Send on Behalf/Send as Permissions
You may want to give user's permissions to send on behalf or send as another mailbox. This can also be done through the Hosted Services Control Panel
Full access permissions
Log into the Control Panel and click Exchange.
Select the user you want to have permissions over. Click on Permissions.
Click Grant permissions.
Select the users which you want to have the ability to view, delete and move items in the mailbox.
Under the Control Panel click the user you want permissions over.
Click Permissions then Send Permissions.
Click Grant Permissions.
From the drop down box next to the users select which kind of permission you want to grant the user over this mailbox.
Send As: the users selected will be able to send as the mailbox.
Send On Behalf: when a user sends as this mailbox the sender will appear as "Mailbox A sending on behalf of Mailbox B".
Click Submit to complete the action.