Is a woman's saying to her husband, who had intercourse with her and did not perform ghusl before Fajr: "It is not permissible for you to fast as long as you have not performed ghusl," correct or incorrect, and does she bear sin for that if it is incorrect?

Janabah (ritual impurity due to sexual discharge) does not affect the validity of the fast. The fast of one who became impure at night and did not perform ghusl until after Fajr is valid. The questioner must repent for speaking about Allah's religion without knowledge, for speaking about Allah without knowledge is among the gravest sins. Her husband must also repent and make up the day he broke his fast, because he was negligent in seeking a fatwa. Issuing a fatwa without knowledge is forbidden and is among the major sins. The sin for this falls upon the one who issues the fatwa if the questioner was not negligent in seeking out qualified scholars for a fatwa; otherwise, the sin is upon both of them.