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I understand that you want to backup an Azure VM to another subscription using PowerShell. Its not currently possible to backup a VM directly to another subscription. Please check to see if one of these options work for you.
Currently Azure Backup allows for Cross Subscription Restore for Azure VM but not direct backup to another subscription. For successful backup, virtual machines must be in the same subscription as the vault for backup. Cross Subscription restore is enabled by default. For the PowerShell instructions on restoring a VM you can refer to the examples here.
Another option is to create an Image of the Virtual Machine in Azure Compute Gallery and share that to the other subscription. If you want the image to be copied to an Azure Compute Gallery in the other subscription you can follow the steps outlined in this blog post.
Hopefully one of these scenarios work for you. If you still have questions or need more assistance please let me know!
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