Is it permissible to have intercourse with one's wife if brown blood appears after the cessation of her menstrual period, following the forty days (postpartum bleeding) and the discontinuation of breastfeeding?

The age of forty is not an age of despair, and the cessation of menstruation might be due to breastfeeding. If the question refers to the fortieth day of post-natal bleeding (nifas), then blood after purification could be menstruation or irregular bleeding. The presence of blood indicates a lack of purification, and purification is achieved by dryness (al-jufūf) or the white discharge (al-qaṣṣah al-bayḍā’). If the blood seen by the questioner continues for twenty-four hours or more, it is menstruation, which prevents prayer, fasting, and intercourse. If it is less than that, it is not menstruation. If she sees the white discharge after menstruation, then anything that exits thereafter is not considered menstruation. Similarly, if she sees dryness after the end of her usual period, she should perform ghusl, and anything that descends afterward is not considered menstruation.