Is it permissible to divorce an American wife in absentia after a separation of one year and an inability to communicate with her, especially if announcing the divorce in the husband's country would harm his social standing, and can she be divorced by a Sharia-sanctioned ma'dhun in another country?

For a Shariah-compliant divorce to be valid, it is not a condition that it be issued by a court or an authorized official, nor is it a condition that the wife be aware of it. Rather, it takes effect simply by the husband uttering the divorce pronouncement. This is concerning the matter between him and his Lord. However, judicially, it is not established except with evidence. If the wife denies the divorce, her word is accepted unless the husband provides evidence of its occurrence. It is advisable to document the divorce or establish evidence for it to avoid future claims from the wife.