When migrating a shared mailbox to Office 365, the following folders may not have permissions set and may not be visibile when opening a shared mailbox in Office 365:
Drafts
Sent Items
Deleted Items
Per Microsoft's recommendation, we use EWS to set folder permissions on O365 mailboxes. EWS only allows permissions to be set for the Calendar, Contacts, Inbox, Journal, Notes, and Tasks folders. EWS unfortunately does not allow for more granular control of permissions, nor does it allow us to set the FullAccess permission on the mailbox.
WORKAROUND
None
STATUS
This currenly not on the roadmap to be addressed.