(No major change in WS2019)Server 2012 overcomes the Quick Storage Migration limitation seen with 2008 R2 (where you can initiate a Storage Migration while the vm remains running for the majority of the transfer but the virtual machine must be powered off at the end of the migration). Hyper-V in Windows Server 2012 introduces support for moving virtual machine storage while the virtual machine remains running. You can perform this task by using a new wizard in Hyper-V Manager or by using new Hyper-V cmdlets for Windows PowerShell. You can add storage to either a stand-alone computer or to a Hyper-V cluster, and then move virtual machines to the new storage while the virtual machine(s) continue to run.You can also perform a live migration of a virtual machine between two non-clustered servers running Hyper-V when you are only using local storage for the virtual machine. In this case, the virtual machines storage is mirrored to the destination server over the network, and then the virtual machine is migrated, while it continues to run and provide network services (shared nothing migration).
Microsoft, HyperV/2019, DataCenter
Storage Migration, VM Mobility, VM Mobility and HA