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The current budget owner should be able to assign this role to another user having the "Create and Own Budgets" app permission.
Jet Hub Administrators are the only users permitted to change the owner of a budget in Jet Budgets. Perhaps the current owner of the budget has the best understanding as to when an owner change is necessary as well as who the criteria for determining the new owner.
The current configuration of limiting this permission to Jet Hub Administrators only has the capacity to be a bit overly restrictive.