Is it permissible to marry a woman who was divorced from her husband at her request because he engaged in illicit sexual acts with her, and she wishes to marry the questioner, while both parties are aware that their current relationship displeases Allah?

Your relationship with this woman is forbidden, especially if it involves incitement against her husband (takhbib), which is one of the major sins, according to the Prophet, peace and blessings be upon him: "He is not of us who incites a woman against her husband." Some scholars have even gone so far as to say that the marriage of the inciter to the incited woman is invalid as a punishment for him. Therefore, you must sever this relationship and repent to Allah. If the woman seeks a divorce (khula') or is divorced and her waiting period ('iddah) ends, then you may marry her after that.