Is it permissible for a friend who has one testicle and a potential for procreation—known only to Allah—to marry without informing his wife of this fact?

If the defect affects intercourse or procreation, the fiancée must be informed, because concealing it is deceit and fraud. The purposes of marriage include enjoyment and procreation. It has been previously stated that any defect found in one of the spouses that negates the purpose of marriage grants the other party the right to annulment. This includes castration and infertility. Ibn Qudamah said: "Castration is a defect that warrants annulment." Therefore, your friend should consult a specialized doctor. If it is confirmed that it affects procreation or intercourse, he must inform his fiancée; otherwise, he is not obliged to. If he conceals it, he is deceitful, and his wife has the option to annul the marriage. If it is confirmed that it does not affect these, he is not obliged to inform her.