Is it obligatory for the wife to prevent her husband from listening to a colleague who commits major sins and speaks about them boastfully, and what should the wife do about that?

Your husband should stop listening to the man who is luring her into the forbidden (haram). His conversations with this man should be limited to offering advice and forbidding evil (munkar), because a companion can pull one along, and Satan has steps that lead to the forbidden, as stated in the verse: "And do not follow the footsteps of Satan. Indeed, he is to you a clear enemy." He should also remind her of Allah, the Last Day, Paradise, and Hellfire, and that one who openly commits sins is in great danger, as the Prophet (peace be upon him) said: "All of my nation are forgiven except those who commit sins openly."