(a) Before the 21st day after the date a will has been probated, the court shall grant letters testamentary, if permitted by law, to each executor appointed by the will who:
(1) is not disqualified; and
(2) is willing to accept the trust and qualify according to law.
(b) Failure of the court to issue letters testamentary within the period prescribed by this section does not affect the validity of any letters testamentary issued in accordance with law after that period.