A husband is an online teacher who teaches men and women. The structure of the class is that his students does not see him, but they see him. They may purchase books from him for his class or find those specific books online for free. They take down notes on what he is writing in the background and sometimes he will allow each of them to repeat through a microphone on what he just went over with them to make sure that everyone is on the same page. He told his students that if they ever have any questions outside of class, they can send in a message to him. However, he also has another job and a family to look after. He sometimes will receive a bunch of questions from his students. When he tries to answer them, his wife will approach him and investigate what he is doing. He tried to be rational with her that these questions are from his students. His wife announced to him that she does not like him to answer any of his women student's questions, but she does not have a problem of him answering any of his men student's questions. He would like to know would it be permissible for him to keep this a secret from his women student's that his wife has a problem of him answering their questions, although they are speaking within the Sharia?
All perfect praise be to Allah, The Lord of the Worlds. I testify that there is none worthy of worship except Allah, and that Muhammad is His slave and Messenger.
It is permissible for the male teacher to answer the questions of his female students as long as he abides by the limits of the Sharee'ah. His wife has no right to prevent him from doing so, and he does not have to inform her about these correspondences and it is permissible for him to hide them from her.
Allah knows best.
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