To be able use VSS based backups of Hyper-V VMs using Windows Server Backup, we need to add the following registry keys to register the Hyper-V VSS Writer with Windows Server Backup. WindowsServerBackup key is not created when we install the Windows Server Backup feature. We have to create this key manually.
When the keys listed above created, we also need to create a String Value with the following parameters / settings:
Name: Application Identifier
When backing up virtual machines, we must select all volumes where VM related files is present, because Windows Server Backup only supports volume based backups.
For more information about Hyper-V virtual machine backups, take a look on the KB958662.