Is it permissible to have intercourse with one's wife after her menstrual bleeding has stopped and ceased, and then blood emerges from her one day after intercourse, bearing in mind that she had given birth approximately 45 days prior, and does this entail a specific action?

There is nothing upon you if you had intercourse with your wife after the cessation of blood and upon her purity, because you had intercourse with her during a valid state of purity. The maximum duration of postpartum bleeding (nifas (definition)) is forty days. If the blood continues beyond that, it is considered irregular bleeding (istihada), unless it coincides with her regular menstrual period, in which case it is considered menstruation. This applies to blood that reappears after its cessation: if it coincides with her regular period, it is menstruation; otherwise, it is irregular bleeding (istihada). Many scholars hold the view that the maximum duration of postpartum bleeding (nifas) is sixty days.