As you may be aware that azure VM is identified with its unique instance ID in a subscription, hence VM backup can only be done in its own subscription. It is not possible to backup a VM to another subscription. This is documented in the azure VM backup support matrix https://learn.microsoft.com/en-us/azure/backup/backup-support-matrix-iaas#supported-backup-actions
Another workaround is to use Azure Site Recovery to maintain a replica of the VM in a different subscription. However the replication approach is different from backup. You may want to take a look at the document link below for details
https://learn.microsoft.com/en-us/azure/site-recovery/azure-to-azure-architecture
https://learn.microsoft.com/en-us/azure/site-recovery/azure-to-azure-tutorial-enable-replication
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