All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad, sallallaahu ‘alayhi wa sallam, is His slave and Messenger.
First of all, we thank and praise Allaah Who guided you to Islam and we ask Him to make you firm and steadfast on His Religion until the Day you meet Him.
We advise you to seek beneficial knowledge, perform good deeds and befriend righteous and pious women, as these are the best things that help a Muslim woman remain steadfast on her religion.
Indeed, you did well by being steadfast on your religion; so we advise you to continue doing so.
You should know that when a woman embraces Islam while being married to a non-Muslim, her marriage contract becomes invalid. Therefore, she is obliged to immediately separate from him and not allow him to have sexual intercourse with her. If he embraces Islam while she is still in her waiting period, then she would still be considered as his wife without having to renew the marriage contract. However, if he does not embrace Islam until her waiting period expires, it becomes permissible for her to marry another man; for more benefit, please refer to Fatwa 84226.
Therefore, if the matter is as you mentioned, that this man is still a non-Muslim, and your waiting period had expired, then he is no longer your husband and it is forbidden for you to let him have sexual intercourse with you. In this case, you are religiously permitted to marry another man even if the divorce procedures are not yet finished.
As regards authenticating the marriage contract [in the court or municipality], then this is not a condition for the validity of the marriage contract.
However, you should take all precautions to avoid any difficulty or problem since you are legally [according to the laws of the country] still considered his wife [but not religiously].
For more benefit, please refer to Fatwa 89381.
Finally, it should be noted that you should ignore the statements of those who claim that you are still his wife despite him still being a non-Muslim, or those who say that you cannot marry another man.
For more benefit, please refer to Fatwa 86524.