Is a wife considered Islamically divorced based on a ruling by an American court, even if the husband did not divorce her Islamically?

The reason for the wife's belief in her husband's disbelief and her separation from him is not clear, and the default is the validity and continuation of the marriage. Divorces issued by man-made courts have no legal standing, and a woman proceeding to marry another man while still married is invalid and reproachable, as per "and [forbidden to you are] the married women" (An-Nisa: 24). Her brother's assistance in her separation is a form of incitement (takhbib). It is advised to consult Islamic centers for assistance in reconciling with the wife. It is impermissible to resort to man-made courts except out of necessity, and if they rule contrary to Islamic law, it is not permissible to accept their ruling.