Hi Make,
If the site mailbox is created, it will be in Active Users, not shared mailboxes.
According to the error message, you can add the affect user to the Owners group or the Members group for the site collection or subsite and check how it works.
Here are the steps:
1.Browse to the site or site collection where you created the site mailbox.
2.Click the gear icon for the Settings menu, and then click Site settings.
3.Click Site permissions.
4.On the ribbon, click Grant Permissions.
5.Click SHOW OPTIONS, select the Members or Owners group permission level, enter the name of the affected user, and then click Share.
If the issue persists, I suggest you use the admin account the set the language via
PowerShell and check again.
Run Set-MailboxRegionalConfiguration -Identity <site mailbox name> -Language <culture info for the mailbox>
For example: Set-MailboxRegionalConfiguration -Identity <site mailbox name> -Language EN-US
For more details about the cmdlet, please refer to:https://technet.microsoft.com/en-us/library/dd351103(v=exchg.150).aspx
Thanks,
Franky