Hi @David Carico ,
I did the similar tests in my environment and got the same issue as you.
Can you successfully send emails with the "Send As" permission of the Shared Mailbox from your OWA?
If it can work fine on your web mail, we may refer that the permission has been successfully granted. As I know, it may take some time for the server permissions to be synced to your local Outlook client. And my error is also caused by this factor. After waiting for a while, I can successfully do it from my Outlook desktop client. By the way, in order to minimize the time required for sync, it is suggested for you to turn off your Cached Exchange Mode(uncheck Use Cached Exchange Mode option) and restart your Outlook to see if your issue has any difference.
If you cannot send the same emails from your OWA either, I'm afraid there might be something wrong with your permission. If this is your case, it is suggested for you to re-grant the permissions via Exchange PowerShell and see if this issue could be resolved.
For more information, please check:
Connect to Exchange Online PowerShell
Add-RecipientPermission
Hope this can be helpful.
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