Due to incompatibility between these services such operations can only be performed via your machine. Direct cloud to cloud backups are not possible between different types of storage providers.
James, I am pretty sure that product uses a service that facilitates the transfers and all data is pulled down to the local computer before being sent to the secondary cloud storage account. If accurate, this is similar to what we do with CloudBerry Backup when you create a Cloud-to-Cloud backup plan. If you were using a cloud service that support infrastructure-as-a-service, you could run a Windows VM with CloudBerry Backup at the source or target to be able to do this all within the cloud, but there would be additional charges for that option and the data would still need egress before moving to the secondary cloud storage.
Have you tried using CloudBerry Backup's Cloud-to-Cloud option using Simple Backup Mode? If so, did it meet your expectations? If not, how would you like that feature improved?