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 is His slave and Messenger.
First of all, it should be noted that a Muslim man or woman should be careful about marrying a recent convert to Islam unless believes with probable cause that he or she is sincere in that. In embracing Islam, it is not enough to utter the Two Testimonies of Faith without abiding by the rites of Islam. Indeed, many people pretend to embrace Islam with the intent of marriage and then it becomes clear that they are not sincere in claiming to be a Muslim. This is speaking in general terms. For more benefit, please refer to Fatwa 86498.
As regards the man in question, then if he had embraced Islam and had abided by the rites of Islam in general, then this woman should not doubt that he is Muslim. Him abandoning the prayer may be due to his ignorance that the prayer is an obligation or due to his laziness in performing it without denying that it is an obligation. This alone does not take a person out of the fold of Islam according to the view of the majority of the jurists. Also, if he says some statements that are considered an act of disbelief, then he is excused for his ignorance because he is a new Muslim. In this case, he should be advised and taught.
Therefore, if he married that woman while fulfilling the conditions of a valid marriage contract, then it is a valid marriage. Now, if the two spouses wish to renew their marriage contract in order to be on the safe side, then no 'Iddah (waiting period) is needed, and also they do not need to wait for Istibraa' (to give birth or make sure that the wife is not pregnant).
Allaah Knows best.