A suggestion to help you might be to upload the files with help of the UploadFromStream() method in the blobs storage SDK. To implement this method, you need to know the Container Name, Archive Storage Account, and Storage Key.
As the method demands the usage of custom coding, you can leverage third-party tools like Cerebrata (https://cerebrata.com/). The tool basically allows you to upload files of any size and also provides options to customize the chunk size, overwrite behavior, file extension, and block blob access tier.
upload files - Azure Storage