How did the murder in the hotel happen?

After a big case was settled, Detective Jones, who was exhausted physically and mentally, went to a famous scenic city in the Mediterranean for a holiday. He lives on the second floor of a hotel and plans to have a good rest for half a month.

But the case followed. On this day, a woman's cry for help suddenly came from the corridor of the hotel. Detective Jones followed the sound and saw a young woman crying in room 2 13. Detective Jones went over, looked through the open door and saw a man lying dead in an easy chair in the room. Detective Jones made a simple examination of the body and confirmed that the man had just died and the bullet had passed through his heart.

Soon, the local police station also sent someone. The woman cried and said, "Someone knocked at the door a few minutes ago. As soon as I opened the door, a masked man outside the door shot at my husband without saying anything, then threw down the gun and ran away. " As the wife of the deceased said, there is indeed a silencer pistol on the carpet in the room. A shell casing landed not far from the left side of the gun, and there was a bullet hole in the wall behind the deceased.

Detective Jones immediately told the local police officer, "Please take this lady back for questioning."

Why do detectives have doubts about the deceased's wife? As a result, there was something suspicious in the wife's words. If, as she said, the gangster shot at her husband outside the door, the shell would not have landed in the room or on the left side of the pistol, because the shell flying out of the pistol should have landed on the right rear of the shooter.