Woman marrying her first husband after taking khula from her second husband

If the first husband gave her one or two talaaqs, and thereafter she remarried and did khula with the second husband, it will be permissible for her to remarry the first husband. However, if the first husband gave her three talaaqs, and thereafter she remarried and did khula with the second husband, she can only remarry the first husband on condition that the nikaah with the second husband was consummated. If the nikaah was not consummated, she will not be halaal for the first husband.

And Allah Ta'ala (الله تعالى) knows best.