Microsoft Exchange Web Services are the key element of proper LMS and your Office365 tenant integration.
In practice this means that your system needs Microsoft.Exchange.WebServices.dll file installed in Windows assembly cache.
In the attachment you can find gacutil.exe (Global Assembly Cache Tool) and Microsoft.Exchange.WebServices.dll. You'll need to unzip the archive and then run gacutil from the Command Prompt and install .dll file manually using the following command:
./gacutil.exe /i Microsoft.Exchange.WebServices.dll
To check if this operation completed successfully you can go to C:\Windows\assembly and make sure that Microsoft.Exchange.WebServices.dll is present there.
For more information about gacutil, please visit this MSDN page.