A new version of Azure AD Connect has been released (version 1.1.524.0) and apart of many bug fixes, there is a lot of improvements.
One of them is the ability to synch Exchange Mail Enabled Public Folder.
You can download the new version here http://go.microsoft.com/fwlink/?LinkId=615771
Please note that there will be a full synchronization after the upgrade because of schema updates.
This does not create public folder in Exchange Online; it just makes your On Premises Mail Enabled Public Folders available in the directory based edge blocking (see https://go.microsoft.com/fwlink/p/?linkid=844910). You also need to ensure the Microsoft Exchange System Objects is selected for synchronization.
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