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Exchange server with working mail flow(internal and external)
Exchange server accepted domain(vanity) should be set to Internal relay
Running DirSyc with Office 365
On the Prem, you need to be assigned permissions before you can perform this procedure or procedures. To see what permissions you need, see the “Mailbox Move and Migration Permissions” section in the Recipients Permissions topic.
Hybrid deployment is configured between your on-premises and Exchange Online organizations.
If you’re running Exchange 2013, make sure the Mailbox Replication Proxy Service (MRSProxy) is enabled on your on-premises Exchange 2013 Client Access servers.