This note studies the posture control problem of a two-link free flying Acrobot with nonzero initial angular momentum, where the control objective is to design an acceleration based control law such that the robot can pass through a desired posture at a given time. Based on the previous results, this posture control problem can be tackled by solving the problem of stabilizing the origin of a system obtained via an appropriate coordinate transformation. The main contribution of this note is to provide a control scheme which globally asymptotically stabilizes the origin of the system. The numerical simulations are given to validate the provided theoretical results.