In order to send email from an address other than your own, you will first need to have "Send As" permissions for that address.
To send email from a departmental mailbox and have the sent message be saved into that account's Sent Items folder, followinstead to access the shared mailbox.
- Begin a new email in Outlook Web App (OWA).
- Click the ... icon and then choose Show From.
- This will add the From field to the email composition window.
- Click on From field and then select Other email address.... Then start typing the email address from which you wish to send your email. You can also click the Search Directory to find the address.
- You will now see the address you chose in the From field. Continue creating your email and send it as normal when ready.