Must the woman pay back the dower to the first husband if she was returned to him after marrying and separating from the second husband?

Supporting text

Al-Qadi mentioned that she owes him a dower. This is the view of some Shafi'i scholars, as she has admitted wrongfully preventing him from having conjugal relations, similar to when divorce witnesses retract their testimony. Our evidence is that her right to the dower was established, and it is not retracted from her, analogous to when she commits apostasy, embraces Islam, or kills herself. If the first husband dies while she is in the second marriage, she should inherit from him due to his admission of her being his wife, or her admission of that fact. If she dies, the second husband does not inherit from her because she is not credited with invalidating the second husband's marriage. The second husband inherits from her because she admits to the validity of that marriage. If the second husband dies, she does not inherit from him because she denies the validity of his marriage.