Using Outlook for iOS in business environments for email and scheduling
I just figure out what happened in my case.
I had the same problem, when I sync IMAP im my Outlook 365 everything works fine, I receive all my inbox messages, but none of my sent items.
So, a strange thing happened when I sent new messages the sent itens from outlook receive the new mails, but the old ones aren't there.
I noticed the sent itens used by my phone (I use Spark on iPhone), created another sent itens folders.
So I just goes to my account name / email on folder left panel, right click, IMAP Folder -> Query -> Subscribe all folders and voilá, two sent items folders...