Using Outlook for iOS for personal email and calendar management
Not sure if you're still having this issue, but maybe this might help out. I had the same situation happen with a couple users when I tried adding them to a shared mailbox. I've scoured forums and didn't find any answers, but I found a solution to it.
In the Outlook mobile app, go to settings, then under Email Accounts, tap their primary email, scroll down and have them remove their primary account. When they log back in, they will be able to add the shared mailbox.
The issue that happens is that when users change their password after logging into the Outlook mobile app, say for example when they work for an organization, they sign in once on their work phone and they never have to sign in again regardless of password change, they still remain logged in with the credentials from their initial log in. So when a Shared Mailbox is created, it's using their current password credentials which doesn't match the log in credentials from the first sign in.
Source: Trust me bro