"Naksu"'s body was FROZEN when Gil-mu stole her from Songrim. Jin Mu asked the King to allow Cheonbugwan to burn her body in public because "the people are troubled by this sorcery." but he kept it on ice. Jin Mu is the master of illusion because of sorcery (his mage powers appear to be low-level) and his enchanted sword so the body that burned was an illusion.
However, up until now, Jin Mu believes that the soul of "Naksu" is lying at the bottom of Lake G in the body of Ae Hyang (the courtesan). EDIT: if there is a soul in Cho-yeong's frozen body, it is the soul of Ae Hyang (the courtesan). So, it will be interesting to find out why he believes "Naksu" is now in Jin Bu-yeon's body.
Reminder: Naksu is not a real person. Her persona as the "Shadow Assasin" was a creation of Jin Mu. Her body is Cho Yeong's. I think he believes that he can brainwash her into using her sword to kill Jang Uk and then people around him will kill her so he's rid of her for good. On her death bed, JBY shifts "Naksu" into Cho Yeong's body.
I have believed the frozen body was lying somewhere at Cheonbugwan from the very beginning. But as for the rest, I hate it because I want Jung So Min to return.
