Unfortunately, it's not completely straightforward when it comes to allowing your users access to shared mailboxes from mobile devices. The model of granting permissions to a shared mailbox to other users, then allowing access using their normal credentials doesn't extend to ActiveSync clients.
This presents challenges because it means that even if you grant a mailbox user access permissions to a shared mailbox, they can't simply add it to their iOS device as an additional mailbox and begin to access the shared mailbox on the move.
Additionally, some of the great features associated with shared mailboxes, such as the ability to automatically map shared mailboxes in Outlook when a user is granted permissions, don't extend to iOS devices either; so there isn't a way to get a user setup with access to a mailbox from a mobile device without further configuration, either by the system administrator or the end user themselves.
However, these challenges...