Even though there is an enable/disable option for VM backup there is no option to resume it. Recovery backups do not support backups cross subscription. So, if you're planning to move your VM to another subscription and then resume the backup that is not possible.
You can follow these steps to move your VM to a new subscription without moving the recover service vault:
- Stop the backup (but only temporarily) and delete the restore point.
- Move the VM and reprotect it under the same vault.
To get more insights on Microsoft Azure, check this Azure course out!