Thaddeus returned to the place where Roderick had met his demise. He didn't have any problem finding it, especially given he'd volunteered to gather the remains when the death was confirmed, remains he'd managed to steal and bring with him when Morpheus betrayed him.
Morpheus probably had a hissy fit when he discovered the box in his possession was a decoy, filled with the useless ash of a campfire. As if Thaddeus would give the real, precious ash to that idiot. He wasn't stupid. Thaddeus knew his enemies would use it against him. Paranoia ever was his best friend.