Send Emails from Another Mailbox or From Address
In order to send emails from another mailbox or address, you will need to first be granted access to the shared mailbox and then will need to add that mailbox to Outlook.
How to Add From Field to Outlook.com
Create a new message in Outlook.com and open the message in a new window
Click Options on the message toolbar and select the From checkbox
You can now change the email address that your email is sent from