Praise be to Allaah.
Ibn Qudaamah (may Allaah have mercy on him) said:
“Chapter Three: if the husband and wife become Muslim together, then they keep their original marriage contract, whether this happens before the marriage is consummated or after. There is no dispute among the scholars on this matter, praise be to Allaah.
Ibn ‘Abd al-Barr mentioned that there is scholarly consensus on the matter. The reason is that there is no difference of religion between the spouses. Abu Dawood reported from Ibn ‘Abbaas that a man came to declare his Islam at the time of the Messenger of Allaah (peace and blessings of Allaah be upon him), then his wife came to declare her Islam. [The man] said: ‘O Messenger of Allaah, she became Muslim when I did.’ So the Prophet (peace and blessings of Allaah be upon him) returned her to him.”
(al-Mughni, part 7, Ahkaam al-Nikaah).
On the basis of the above, their original marriage contract is sufficient, and there is no need for them to do a new one. And Allaah knows best.