Most of the Windows administrators are not aware of procedure to move existing Windows Fail over Cluster File Share Witness directory to new Servers, following is a quick three step guideline.
Step 1: Find out the Quorum Type
Run the PowerShell as Administrator
output: Cluster Name, Quorum Resource and Quorum Type.
Step 2: Change the existing Quorum Type from NodeAndFileShareMajority to NodeMajority
Output: Cluster Name & Quorum Resource Null
The movement the Step 2 get completed successfully it will delete existing FSW from Cluster resource.
Step 3: Recreate FSW with NodeAndFileShareMajority at new Server
Set-ClusterQuorum -NodeAndFileShareMajority \\FileServer\Shared_FSW
After successful completion of step 3 the FSW will get created and ready to use.