It is hereby made the duty of the executor of the estate of any person who has died a resident of Alabama and upon which estate the tax imposed under any federal revenue act has not been paid, and the executor of any person who may hereafter die a resident of this state, and whose estate is subject to the payment of a federal estate tax, to file with the Department of Revenue of Alabama a duplicate of all the returns which he is required to make to the federal authorities for the purpose of having the estate taxes determined. When such duplicate return is filed with the Department of Revenue, it shall compute the amount of tax that would be due upon said return as federal estate taxes imposed under any federal act permitting credit of inheritance or estate taxes to the states upon the property of said estate taxable in the State of Alabama and shall assess against said estate as estate tax for the State of Alabama the amount levied and found to be due under the provisions of such act or acts. If, after the filing of any duplicate returns herein required and the assessment of the state estate taxes, upon basis of return made, the federal authorities shall increase or decrease the amount of the federal estate tax, an amended return shall be filed with the Department of Revenue, showing all the changes made in the original return and the amount of increase or decrease in the federal estate tax, and the Department of Revenue shall assess against said estate the additional amount found to be due hereunder. In the event of a decrease in the federal estate tax, the state shall refund to the said estate its proportion of said decrease.