In order for Ubuntu virtual machine live Hyper-V backup to work properly, you need to install Hyper-V’s Linux Integration Services.
Download the currently latest version 4.1 at https://blogs.technet.microsoft.com/virtualization/2016/03/21/linux-integration-services-4-1/
Then run the commands:
Sudo apt install hv-kvp-daemon-init linux-tools-virtual-lts-xenial linux-cloud-tools-virtual-lts-xenial
Then reboot the VM.
The ISO and RPM files can be downloaded here: https://www.microsoft.com/en-us/download/details.aspx?id=51612
How to Run Automatic Hyper-V VM Backups with Open Source File Formats
Download and run the BackupChain installer to set up BackupChain’s server backup software and enjoy a “vendor lock-in-free” backup environment that works with open standard backup file formats. Virtual servers can be processed with deduplication that greatly minimizes backup storage usage, no matter if you use cloud backup, Hyper-V Linux backup, VMware backup, Exchange backup, and entire file server backups. Apart from server backup, BackupChain also offers various virtual machine backup features for Windows PCs, from XP to Windows 10.