YES , a muslim woman can marry a convert, A Muslim convert is equal to any other Muslim in the eyes of the Holy Qur'an. Furthermore, a convert has more advantages than a born Muslim for two reasons: 1- A convert deserves a bigger reward from God than a born Muslim. A convert becomes a Muslim usually after a great deal of research and some psychological crisis, because changing religion is not an easy task. It takes a great deal of courage and effort on the part of the convert, while a born Muslim receives his religion by inheritance. 2- A convert is considered, by his conversion to Islam, pure and free of any previous sin. All his previous sins are wiped out entirely. He will be responsible only for the sins which he commits after becoming a Muslim. Thus, if a person becomes a Muslim in the early morning, after sunrise, then he dies before noon, he is entitled to enter paradise without having practiced or performed any of the devotional duties which a Muslim is required to do. He did not have to perform morning prayer because his conversion to Islam took place after sunrise, nor did he have to perform the noon prayer because he did not live until noon, the prayer time.