Is it possible to shorten a long jaw to a short jaw like this? (Photo)

Jaw surgery is not done widely. It is common in Korea, but also in Boston at my office where we do what you are requesting 4-5 times each week. It is done through the inside of the mouth so there are no external scars.

What you are asking for is a vertical jawline reduction between the jaw angles and the chin, known as v line surgery. Also the exact look you are showing actually is a jaw angle augmentation with a vertical jawline reduction up to the chin. The key maneuver is to reduce the vertical length of your chin and jawline and not just its width which is likely not a concern since you are only showing the side profile.