A divorced woman who is pregnant marries another man during her pregnancy, then they are separated, and then she gives birth. Does she observe the waiting period for this second man?

The Shaykh : He says: A divorced woman who is pregnant married [another man], then she was divorced from the second man, then she breastfed [or gave birth], then she gave birth. Does she observe the waiting period for the second man? And if she does not observe the waiting period, is the absence of the waiting period due to the invalidity of the contract, or due to the lack of need for purification of the womb, since that is known by her giving birth?
First: This marriage is invalid by consensus, and no waiting period is obligatory for it, even if he had intercourse with her and seclusion occurred. Therefore, no waiting period is obligatory for her because it is invalid. Accordingly, the waiting period is for the first husband.