What is incumbent upon the father and upon the woman who impersonated the wife after the father divorced his wife in absentia, by another woman impersonating the wife, knowing that the location of the divorced wife is currently unknown?

For a divorce to occur, the presence of the wife or her knowledge of it is not a condition. If the father uttered a clear divorce pronouncement, such as saying: "My wife is divorced," then she is divorced from him. If the father brought another woman to impersonate his wife before the official authorities who require the wife's presence, the divorce is still valid for the father's wife as long as he pronounced it. There is no blame on the father for this, because the condition of the wife's presence has no basis in Islamic law. It is a man's right to divorce his wife without her presence, and if he is prevented from doing so, it is permissible for him to use a stratagem. There is no blame on the woman who impersonated the wife if her intention was to help the father obtain his right.