The newest version of Outlook for iOS Application allows for users to open shared mailboxes.
Alternatively, they can map the mailbox via IMAP using the below instructions:
EMAIL ADDRESS: SharedMailboxUPN@austin.utexas.edu (shared mailbox)
PASSWORD: FullAccessMailboxUPN 's Password (user's password)
IMAP SERVER: outlook.office365.com (imap server)
SMTP SERVER: smtp.office365.com (smtp server)
USERNAME: FullAccessMailboxUPN@austin.utexas.edu\SharedMailboxUPN@austin.utexas.edu