I have extensive experience with MS SQL Server, Azure, data loads, and automation. I have worked with many other database vendors too. All told, I have 18 years of experience in migrating data between systems, and automating that process.
The one major unknown in automating what you have described is how you receive the files from your partner. You mention email as an option, so I will base my option below on email. I am a technical consultant, so if you decide to work with me, I can investigate other options for automating the transfer of data.
I would create a C# service that runs on a computer. This computer does not need to be a server, it can be any plain old computer. That service would monitor an email account. When an email arrived, it would save the attachments to the local computer. The service would then massage the documents as needed to match your Azure structure. Next, the service would load the information to your Azure instance. I am assuming that there is sufficient information in the tables provided to determine if an update or insert is required. Of course, the service would email status.
I am all about automation. I hate having to do the same work over and over again, when it could be done automatically. I would be happy to help you out with this problem. As I said earlier, there are many possible solutions to what you have described, I have just picked one.
Carl.