Is one who takes an amount from the inheritance to perform 'Umrah indebted to his siblings for this amount when it is distributed, or for its value equivalent to gold at the time of the inheritance distribution? What is the Sharia ruling on this?

It is not permissible to dispose of the inheritance by borrowing or otherwise except with the permission of the adult, mature heirs. Settling a fixed debt in a currency must be in the same currency, not its value, so it is not permissible to link fixed debts to price levels. What must be settled is the six thousand pounds as they are, not their value in gold.