Azure File Movement

Azure has tools designed to help you move individual files or small file groups.
Tools are AzCopy, Azure Storage Explorer, and Azure File Sync.

Azure AzCopy

AzCopy is a command-line utility that you can use to copy blobs or files to or from your storage account.
With AzCopy, you can upload files, download files, copy files between storage accounts, and even synchronize files.
AzCopy can even be configured to work with other cloud providers to help move files back and forth between clouds.
Synchronizing blobs or files with AzCopy is one-direction synchronization.

Azure Storage Explorer is UI app to manage files and blobs in your Azure Storage Account.
It works on Windows, macOS, and Linux operating systems and uses AzCopy on the backend to perform all of the file and blob management tasks.
With Storage Explorer, you can upload to Azure, download from Azure, or move between storage accounts.

Azure File Sync is a tool that lets you centralize your file shares in Azure Files and keep the flexibility, performance, and compatibility of a Windows file server.
Azure File Sync additionally has the ability to transform Windows Server into a quick cache of your Azure file share.
Once you install Azure File Sync on your local Windows server, it will automatically stay bi-directionally synced with your files in Azure.
You can use any protocol that's available on Windows Server to access your data locally, including SMB, NFS, and FTPS.
Have as many caches as you need across the world.
Replace a failed local server by installing Azure File Sync on a new server in the same datacenter.
Configure cloud tiering so the most frequently accessed files are replicated locally, while infrequently accessed files are kept in the cloud until requested.