Several studies have investigated the influence of appearance and motion of a visually perceivable object, such as a person's image, video, or an avatar in the virtual environment, on the body sense. These studies have primarily examined the effect on the senses of ownership and agency with one's body or with the object while exercising and observing the object in real-time (on-line movement observation). This paper examines the influence of the appearance and motion of an avatar object on recognizing the agent of the object's motion (self-body recognition), when the timings of self-exercising and observing the avatar's motion are different (off-line movement observation). Obtained experimental results show that the visual motion of the avatar has a significant effect on self-body recognition with the avatar. Furthermore, the effect of the avatar's appearance on self-recognition can vary according to the person's gender. It has also been found that increased self-body recognition with the avatar can lead to greater number of flaws being observed in the avatar's motion.