Hello Cas B,
Good day! Thank you for posting to Microsoft Community.
I understand that you're experiencing issues with sending emails on behalf of a shared mailbox.
Based on your description, it looks like you need the shared mailbox address to be automatically added to the From field in a new email. I did some tests on my end as well and noticed that outlook will use the address assigned to the currently selected mailbox or data file as the default address if it is configured as an account in File, Account Settings. Because a shared account is a secondary account in your profile, Outlook won’t use that address by default when viewing the mailbox. Looks like a design behavior. Open and use a shared mailbox in Outlook - Microsoft Support.
You can go around this by adding the shared mailbox to your profile as a mailbox. You may however need remove delegate permissions or disable automapping before you add it to your profile.
In case I misunderstood you in anyway, please let me know.
Looking forward to your response.
Best Regards,
Ashraf.