What is the ruling regarding a marriage contract made between non-Muslims if they subsequently embrace Islam or refer their existing contract to a Muslim judge?

Primary text

If the parties embrace Islam or bring their contract before the judge after its conclusion, the judge shall not inquire into the methodology of their contract but shall examine the existing situation. If the woman is one upon whom marriage is permissible to contract initially, the marriage is affirmed. If the woman is one upon whom initial marriage is not permissible, such as a close female relative (mahram), the judge shall separate them.