Is the husband's statement to his wife, "If you speak to anyone online other than your family, you will be forbidden to me, meaning divorced," considered an oath of divorce, and does the divorce take effect if the wife continues to speak to her friends online without his knowledge, knowing that he has never said this to her before?

If the husband says: "If you speak to anyone online other than your family, you will be forbidden (muharramah)," this is a promise of prohibition and has no legal consequence. However, if he says: "If you speak to anyone online other than your family, then you are forbidden (muharramah)," then if she speaks to someone, the prohibition takes effect. The prevailing opinion regarding a husband's prohibition of his wife is that it depends on the husband's intention. If he intended divorce by it, then divorce occurs. However, if there was a reason for the oath and that reason ceased, and then she spoke to someone, there are no consequences for breaking the oath if the swearer had no specific intention. It is obligatory for the wife to obey her husband, and her conversing with non-mahram men is not permissible, and its prohibition is further confirmed by the husband's forbidding it.