Robotic hands embedding human motor control principles in their mechanical design are getting increasing interest thanks to their simplicity and robustness, combined with good performance. Another key aspect of these hands is that humans can use them very effectively thanks to the similarity of their behavior with real hands. Nevertheless, controlling more than one degree of actuation remains a challenging task. In this paper, we take advantage of these characteristics in a multi-synergistic prosthesis. We propose an integrated setup composed of Pisa/IIT SoftHand 2 and a control strategy which simultaneously and proportionally maps the human hand movements to the robotic hand. The control technique is based on a combination of non-negative matrix factorization and linear regression algorithms. It also features a real-time continuous posture compensation of the electromyographic signals based on an IMU. The algorithm is tested on five healthy subjects through an experiment in a virtual environment. In a separate experiment, the efficacy of the posture compensation strategy is evaluated on five healthy subjects and, finally, the whole setup is successfully tested in performing realistic daily life activities.