Microsoft Article on Shared Mailboxes

This type of mailbox shows under your main mailbox in Outlook as a separate mailbox.

To send from it you would have to:

Click on New Email at the top of Outlook

Make sure your inbox selected, click on From, click on Other Email Address.

Type in the username for the email. In this case SMS.

It will populate the email address in the From box.
Send a Test email to your email address.

Once you do that it will have your recent From addresses in the drop down box.