In [H. Rashidi, A. Golchin, H. Mohammadzadeh Saany, On GPW-flat acts, Categories and General Algebraic Structures
with Applications. Vol. 12. No. 1 (2020), pp. 175{197] GPWflatness was introduced. In this article we continue this investigation and will give a characterization of monoids by this condition of their right Rees factor acts.