What should a man do who divorced his wife without informing her, then took her back verbally without her knowledge within two and a half months, then two years later learned that the waiting period ('iddah) is calculated by the number of menstrual cycles, not by months?

The waiting period (iddah (definition)) for a divorced woman with whom the marriage was consummated and who experiences menstruation is three menstrual cycles (quru'). It is not permissible for her to observe the waiting period by months. If a man takes back his divorced wife and asks her about the number of menstrual cycles she experienced from the time of the divorce until the reconciliation: if it becomes clear that he took her back within the waiting period, the reconciliation is valid. However, if it becomes clear that the waiting period had ended before the reconciliation, then the reconciliation is void, and the woman has become irrevocably separated by the divorce. She cannot return to him except with a new marriage contract.