A new birth certificate shall be established by the State Registrar upon receipt of either of the following:
(a) A report of adoption from any court of record that has jurisdiction of the child in this state, another state, the District of Columbia, in any territory of the United States, or in any foreign country, for any child born in California and whose certificate of birth is on file in the office of the State Registrar.
(b) A readoption order issued pursuant to Section 8919 of the Family Code.