When you move a VM from classic to Resource Manager mode, backups taken prior to migration will not migrate to newly migrated Resource Manager VM. However, if you wish to keep your backups of classic VMs, follow these steps before the migration.
In the Recovery Services vault, go to the Backup Items blade and select the VM.
Click Stop Backup. Select "Retain Backup Data" in the dropdown menu..
Note
This option will stop all future backup jobs from protecting your VM. However, Azure Backup service will retain the recovery points that have been backed up. You'll need to pay to keep the recovery points in the vault (see Azure Backup pricing for details). You'll be able to restore the VM if needed. If you decide to resume VM protection, then you can use Resume backup option.
To migrate the virtual machine to Resource Manager mode,
Delete the backup/snapshot extension from the VM.
Migrate the virtual machine from classic mode to Resource Manager mode. Make sure the storage and network information corresponding to the virtual machine is also migrated to Resource Manager mode.
Additionally, if you want to back up the migrated VM, go to Virtual Machine management blade to enable backup.