Is it obligatory for the questioner to expiate his oath and inform the woman's husband of what his wife told him, knowing that it was his wife who anticipated the online communication and not the other woman?

Divorce occurs by an oath of divorce according to the majority of scholars. However, Ibn Taymiyyah holds that if the one swearing the oath did not intend divorce, then he must offer expiation for an oath (kaffarat yamin). If the oath was based on a cause and that cause turned out to be contrary, then whoever considers the cause that prompted the oath will not deem the divorce to occur when the cause is absent. This is the well-known position of Imam Ahmad and the choice of Ibn Taymiyyah and Ibn al-Qayyim. They believe that the intention or the cause are the determining factors in the oath. Therefore, do not tell the woman's husband what she said, and there is no obligation upon you. We warn that swearing by divorce is impermissible.