Does engaging in sexual activity after converting to Islam prevent marriage in the Islamic way, and if so, is there a way to rectify that?

The fornicator must repent from fornication, which is one of the major sins forbidden by Islamic law, and for which Allah has promised severe torment in the Hereafter, and mandated a worldly punishment of lashing or stoning. If the fornicator repents sincerely and truthfully, Allah will accept his repentance and replace his evil deeds with good ones. It is permissible to marry a female fornicator after her repentance and after her womb has been cleansed by one menstrual cycle.