The tax hereby levied, being based and conditioned upon the levy of a similar tax by the United States, in the event that after due return made the final assessment of the tax or final assessment as to the value of the estate for the purposes of such federal tax shall not have been arrived at when payment would otherwise become due or delinquent hereunder, then and in such event the time for payment of the tax due hereunder shall, on showing being made to the Department of Revenue, be extended until final agreement, determination or assessment of the tax or value of the estate for the determination of the tax shall have been made for the purpose of such federal tax; provided, that the Department of Revenue may demand and require the payment of such amount of the tax as it may determine will not be in excess of the total tax that will be due the State of Alabama under this chapter, as shown by the tax return made, when the final determination of the amount of the assessment of the tax shall have been made for federal tax purposes.