Hello @Aditya Sehrawat ,
Welcome Microsoft Q&A forum!
As of today, Azure backup does not support restoring of backed up data stored in a vault (A) to be moved to a different vault (B).
Also, refer to the feedback item - https://feedback.azure.com/forums/258995-azure-backup/suggestions/33419662-move-vm-from-recovery-services-vault-to-new-vault about moving VM from one vault to another. You may want to comment on the same with your business requirement for this feature and up-vote it.
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