Is it obligatory to inform one's wife about a sexual conversation that took place with another girl after marriage, given the intense remorse and determination not to return to this sin?

You must sincerely repent to Allah Almighty for the sin you have committed. Sincere repentance is only achieved by recognizing the danger of the sin, which stands between you and everything you love, and throws you into everything you fear. This generates the fire of remorse within the soul, for remorse is repentance. Sincere repentance has an effect on the past, present, and future: remorse and regret for what has passed, abstaining from the sin in the present, and a sincere resolve not to return to the sin in the future. Conceal your sin and do not tell anyone what you have done; for whoever is afflicted with any of these filthinesses, let him conceal himself with Allah’s concealment.