Hi @ Shadow Rider，
Currently, it's not possible to add a shared mailbox of on-premises Exchange on a mobile device.
And in my tests, adding a shared mailbox to Outlook Mobile also only works for Exchange online account.
Therefore, as a workaround, I recommend that you use OWA or the Outlook desktop app to view the on-prem shared mailboxes.
Here is a similar thread for your reference: Adding Shared Mailbox in Outlook for mobile in Exchange 2019 on-premises - Microsoft Q&A
Hope the above information is helpful to you.
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