In earlier blog post I explained how to create user account on-premises and accompanying Mailboxes in Office 365. This is possible with or without an Exchange server on-premises. The latter works, but it’s not supported.
There are also scenarios where you have cloud identities in Office 365 that you want to connect to user accounts in an on-premises Active Directory, so basically converting the cloud identity to a synced identity. This is a common scenario for example when moving from one tenant in Office 365 to another tenant, of maybe when moving from Groupwise or Notes to Office 365.
Suppose we have a cloud identity in Office 365 for a user named Chong Kim, he has an E3 license, a username firstname.lastname@example.org and this is also his primary SMTP address.