What is the ruling on a woman divorced thrice who intends to marry a man with the intention of becoming lawful for her first husband, without an agreement with the new husband, and with the first husband encouraging her to do so?

There is no harm in a woman intending to return to her first husband after marrying another, unless she agreed upon or stipulated this to the second suitor, because the marital bond is not in her hand, and Allah has forgiven inner thoughts as long as they are not acted upon. It is also permissible for the first husband to encourage her to do so. What is prohibited is for either spouse or both to agree with the second husband with the intention of making her lawful (for the first husband), or for the second husband to have the intention of making her lawful.