(a) No final account of any fiduciary shall be allowed by any probate court of the state, unless such account shows, and the judge of said court finds, that all taxes imposed by the provisions of any state tax law which have become payable, have been paid, and that all taxes which may become due are secured by bond, deposit or otherwise. The certificate of the Tax Commission shall be conclusive as to the payment of any tax, to the extent of said certificate.

(b) For the purpose of facilitating the settlement and distribution of the estates held by fiduciaries, the Tax Commission may, subject to the approval of the court having jurisdiction of any such estate, or as provided by Section 219 of this Code, agree upon the amount of taxes, at any time due or to become due, from such fiduciaries, under the provisions of any state tax law, and payment, in accordance with such agreement, shall be in full satisfaction of all taxes to which the agreement relates.