What is the basis for determining the necessity and extent of replacement for a deceased person in voluntary Hajj?

Primary text

Voluntary Hajj is considered permissible regardless of the starting location. A reliable agent (*mustanab*) may be appointed for the deceased based on the minimum amount available, unless the heirs consent to an increase. If the deceased specified an amount in the bequest, that specified amount is permissible so long as it does not exceed one-third of the estate.