What is the ruling on private correspondence between a woman who has become a supervisor in a women's forum and the forum's administrator, who is a man? And is this considered forbidden mixing?

It is sufficient dispraise for idle talk that it is devoid of religious and worldly benefits. It is befitting for a wise person to abandon it, even if it were permissible, for Allah has praised the people of faith and piety by stating that they turn away from idle talk. A wise person is more covetous of their time than their wealth, for time is their capital and they will be held accountable for it on the Day of Resurrection, as stated in the Hadith: "The feet of a servant will not move [on the Day of Judgment] until he is asked about four things: about his life, how he spent it; about his knowledge, what he did with it; about his wealth, from where he acquired it and in what he spent it; and about his body, how he wore it out." Many people are deceived concerning the blessings of health and free time. And whoever Allah has blessed with free time should utilize it in obedience to Allah. If this is the case for occupying time with purely permissible matters, then what about manifest sins such as a woman corresponding with non-mahram men? Indeed, it is forbidden due to its opening the door to temptations and evils. And do not be deceived by what is mentioned about the content of the messages being within the bounds of etiquette, for Satan entices its parties to fall into the forbidden.