Were the husband's returns of his wife permissible or forbidden after two divorces, and is it permissible for him to return her after the third divorce?

If the husband took his wife back after the second divorce with the sole intention of provoking her, not of reconciliation, then his resumption of marital relations is valid. However, this act is considered transgressing the limits of Allah and an injustice to the wife, and it contradicts His (the Almighty’s) saying: "Divorce is twice. Then, either keep [her] with acceptance or release [her] with good treatment." As for his taking her back after the third divorce, it is not valid, because this results in the major irrevocable divorce (al-baynunah al-kubra), and he cannot take her back unless she marries another man willingly, and the new husband separates from her, and her waiting period (iddah) from him ends.