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Currently it’s not supported to add the shared mailbox in iPhone, since iPhone doesn’t support adding additional account or non-password account in it.
If you want to check mails of the shared mailbox in iPhone, you can try adding the shared mailbox as an connected account in your main mailbox or setting up a forward rule to forward all the mails of the shared mailbox to the main mailbox. After that, you will receive all the mails both sent to the shared mailbox and your own mailbox.
For more details, please refer to the links below:
Connect to another email account
Use rules to automatically forward messages in Office 365