Makes no sense

I'm definitely enjoying this drama, but the whole murderer of the man who forged certificates still makes no sense. If the guy died how did they know her description? Even if he wasn't dead, he apparently had an injury severe enough to cause death, could have actually given it to them in that condition? Also, was he such an important person? It has been at least six months since that happened and they are still actively looking for her. Even nowadays they put a case in the back burner if too much time has passed and six months back then would have been a lot of time I'm guessing.