To obtain a divorce, the husband would need to file a petition with the appropriate court in the state where he resides, and the court would need to have jurisdiction over the marriage. If the wife is not physically present in the United States, the court may require that she be served with legal documents informing her of the divorce proceedings. This can be done through means such as international mail or service through the Mexican government.
The wife would then have the opportunity to respond to the petition and participate in the divorce proceedings. If she does not respond or participate, the court may still grant the divorce, but it would likely require additional steps to ensure that the wife had proper notice and an opportunity to defend herself.
If the wife wishes to contest the divorce or has claims for support or property division, it is important for her to be represented by an attorney in the United States who can protect her rights and interests. In such cases, the divorce proceedings may become more complex and may involve litigation and cross-border cooperation.
Therefore, it is generally not possible for a husband to obtain a divorce in the U.S. from his wife residing in Mexico without her knowing or without taking proper legal steps to notify her and provide her with due process.