Is my father a mahram to the wife of my half-brother through my mother?

He is not a mahram to her, because he (the questioner’s half-brother) is not his son; rather she is the wife of his wife’s son. So your half-brother through your mother is the son of your father’s wife, who is your mother. Therefore the wife of your half-brother through your mother is a “stranger” (non-mahram) to him, and he is not a mahram to her. If your brother divorced her, it would be permissible for your father to marry her, because she is not the wife of his son, and she is not the daughter of his wife, such that she would be his stepdaughter. So he is not a mahram to her; rather she is the wife of his wife’s son, therefore she is a non-mahram to him.

And Allah knows best.