TL;DR

Migration is done via azcopy:

• download souce container to local folder
• upload local folder to destination container

Get AzCopy

Here is the script install-azcopy.ps1:

# Download and extract

#
$URI = "https://aka.ms/downloadazcopy-v10-windows"
$DST = "~\AppData\Local\Programs\AZCopy\"

Invoke-WebRequest -Uri $URI -OutFile AzCopy.zip -UseBasicParsing
Expand-Archive ./AzCopy.zip ./AzCopy -Force

# Move AzCopy
mkdir ~\AppData\Local\Programs\AZCopy
Get-ChildItem ./AzCopy/*/azcopy.exe | Move-Item -Destination "~\$DEST"

# Add AzCopy to PATH
$userenv = (Get-ItemProperty -Path 'HKCU:\Environment' -Name Path).path
$newPath = "$userenv
New-ItemProperty -Path 'HKCU:\Environment' -Name Path -Value $newPath -Force

# Clean the kitchen
del -Force AzCopy.zip
del -Force -Recurse .\AzCopy\

Copy Folder

param (
    $FOLDER = "",

    [Parameter(Mandatory=$false)]
    [string]$TYPE   = "latest",

    [Parameter(Mandatory=$false)]
    [switch]$LOGIN
)

if ($TYPE -eq "latest") {
    $SRC_ROOT="<latest-folder>"
    $DST_ROOT="latest"
} else {
    $SRC_ROOT="<history-folder>"
    $DST_ROOT="history"
}


$SRC_ACCCOUNT = "<source storage account>";
$DST_ACCCOUNT = "<destination storage account>";

$SRC_CONTAINER = "<source container>"
$DST_CONTAINER = "<destination container>"


$SRC_URL      = "https://${SRC_ACCCOUNT}.blob.core.windows.net/$SRC_CONTAINER/$SRC_ROOT/$FOLDER/"
$DST_URL      = "https://${DST_ACCCOUNT}.blob.core.windows.net/$DST_CONTAINER/$DST_ROOT/"

$TMP_FLDR     = "C:\TMP\Downloads"

Write-Host  "== Copy     '$FOLDER'"
Write-Host "       from  $SRC_URL"
Write-Host  "        to  $DST_URL"

#

if ($LOGIN) {
    $ENV:AZCOPY_CRED_TYPE = "OAuthToken";
    $ENV:AZCOPY_CONCURRENCY_VALUE = "AUTO";

    azcopy login
}

Write-Host  "== Download ======================================================"
Write-Host "       from  $SRC_URL"
Write-Host  "        to  $TMP_FLDR\$CONTAINER"

azcopy copy         $SRC_URL                                                                                      `
                    $TMP_FLDR                                                                                     `
                    --trusted-microsoft-suffixes=${SRC_ACCCOUNT}.blob.core.windows.net                            `
                    --overwrite=true                                                                              `
                    --check-md5=FailIfDifferent                                                                   `
                    --from-to=BlobLocal                                                                           `
                    --recursive                                                                                   `
                    --log-level=ERROR

# Upload
Write-Host  "== Upload   ======================================================"
Write-Host  "      from  $TMP_FLDR\$CONTAINER"
Write-Host  "        to  $DST_URL"

azcopy copy         $TMP_FLDR\$CONTAINER                         `
                    $DST_URL                                     `
                    --overwrite=true                             `
                    --from-to=LocalBlob                          `
                    --blob-type BlockBlob                        `
                    --follow-symlinks                            `
                    --check-length=true                          `
                    --put-md5                                    `
                    --follow-symlinks                            `
                    --disable-auto-decoding=false                `
                    --recursive                                  `
                    --log-level=ERROR

Call the script

First call should use -login to authenticate

.\copy.ps1 demo-folder-1 -login

Then, following commands dont need the login

.\copy.ps1 demo-folder-2