Migrating shared mailboxes to Office 365 is one of those things that is starting to become easier over time, especially with full access permissions now working cross premises.
One little discovery that I thought I would share is that if you have an Exchange 2010 hybrid configuration, the auto mapping feature will not work cross premises. (Exchange 2013 and above, you are ok and have nothing to worry about).
This means if an on-premises user has access to a shared mailbox that you migrate to Office 365, it will disappear from their Outlook even though they still have full access.
Unless you migrate the shared mailbox and user at the same time, the only option is to manually add the shared mailbox back into Outlook.
Something to keep in mind especially if your user base accesses multiple shared mailboxes at a time.