Is it permissible, in Sharia, to exhume the deceased's body for an autopsy to determine the cause of death, especially when there is strong suspicion that the wife murdered her husband?

The default ruling is that it is forbidden to dissect the body of a Muslim, as the sanctity of a Muslim after death is the same as during life. Dissecting a Muslim's body is not permissible except in cases of necessity. Your suspicion regarding your brother's wife does not justify violating his body through dissection, especially since the suspicion is not based on reliable evidence; rather, it stems from ill-conjecture, which is forbidden.

Ibn Uthaymeen said: "A Muslim's blood, wealth, and honor are sacred, and a Muslim is to be respected in life and after death. Breaking the bone of a deceased person is like breaking it while they are alive." Therefore, dissecting a Muslim's body is not permissible except for a need or necessity. What you mentioned about the woman does not constitute evidence that she committed the heinous act. Fear Allah, do not harbor ill thoughts, and do not harm your brother's body.