Robotic prosthetic hands can help perform the intended sophisticated movements of the upper limb, which can assist amputees to perform their daily activities. Although a robotic prosthetic hand can be controlled in real-time using the user's electromyography (EMG), which directly reflects the user's motion intention, some important EMG signals are usually lost owing to muscle deficiency. This study proposes a muscle activity estimator that is inspired by the muscle synergy across subjects to estimate the activity of the missing muscles in amputees in real-time. The proposed estimator learns muscle synergy from the EMG balance, finger joint angles, and the grasping force of healthy persons. The proposed estimator is developed as an artificial neural network (ANN) with a novel cell structure that combines long-short-term memory and damping neurons to analyze muscle dynamics. Furthermore, to improve the accuracy of learning muscle synergy, the muscles to be input to the estimator are selected by focusing on the enslavement of muscles and anatomical relationships. The effectiveness of the proposed estimator is evaluated by experiments. The results showed that the proposed estimator can contribute well to the realization of the intended sophisticated motions of the user.