We're working on bringing the 2017-04-17 version of the Azure Storage API to use in Azure Stack. When ready, this will enable Azure Stack users to perform URL-to-URL copies, simplifying the movement of data between Azure and Azure Stack. This update applies primarily to Azure Stack users, but will be beneficial to any user looking to create hybrid applications that span Azure and Azure Stack.
Get more information about Azure Storage on Azure Stack.
See more about Azure Stack roles and responsibilities.
Source: Azure Roadmap