A brute-force method for copying files is to download them locally and the upload them to target region using Azure Storage Explorer.
Microsoft offers another tool called AZCOPY that allows you to move files between storage accounts and between regions (as well as upload/download to you).
AZCOPY was originally for Windows only, but a recent version has been created for Linux/Mac.
Here are three links that you might find helpful:
AZCOPY for Windows
AZCOPY for Linux
AZCOPY for Linux/Mac