UPDATE 09/11/2016

Delegated access applies only for full access; send-as, send on behalf or delegation from Outlook do not work. Cross-premises permissions do not work in OWA

Details https://technet.microsoft.com/en-us/library/jj200581(v=exchg.150).aspx

 

This has been a major limitation of the Exchange Hybrid mode for quite long time.

I just noticed that you can now have access to a delegated mailbox hosted on premises if your mailbox is on Office 365, and the other way too.

I don’t know since then neither what is the prerequisites to get it working.

To give you a starting point, I’m running Exchange 2016 CU3 with Azure AD Connect version 1.1.281 (off course configured with the Exchange Hybrid option enabled)

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The main mailbox is hosted on premises and the delegated is hosted on Exchange Online

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The main mailbox is hosted on Exchange Online and the delegated is hosted on premises

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