Based on our paper (I), we calculate the free energy of the hydrogen-bond ferroelectrics system with four-body interactions, and propose the conditions to determine the Curie temperature and the discontinuity of the first order phase transition. The detailed analysis of free energy around the transition temperature indicates that the results of our microscopic model coincide with the predictions of Landau's theory. And the relations between the coefficients in Landau free energy and the microscopic interaction constants are obtained, that makes the physical meaning of these coefficients more clear. By comparing with the experimental data of PbHPO4, PbDPO4 and H2C4O4 crystals, we confirm that our theory can successfully explain the first order ferroelectric phase transition as well as the second order transition.