What's the application used for, are you using this application to send messages through Exchange server? Please provide more information about the relationship between this app and exch server.
Ganerally the configuration in below link help us set SMTP Application Relay in on-premise Exchange
In addition, I'm not very clear about the point you mentioned above: We will have a local domain controller in Azure on VM? Do you mean you are going to add a new DC in Azure, you want to keep the DCs on both sites or etc?
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