We have investigated the dynamics of magnetization under a current pulse in a φ0 - junction with a direct coupling between the magnetic moment and the superconducting current. The correspondence between the magnetization value at the end of the pulse mz * and the realization of the magnetization reversal along the easy axis of the ferromagnetic is considered. The crucial influence of the ratio w of the ferromagnetic frequency to the characteristic frequency of the Josephson junction on the results of reversal predictions is demonstrated. Effect of w magnitude on the manifestation of periodicity bands in the mz * dependence on the model parameters is shown. There is a critical value of the Gilbert damping, above which the magnetization reversal is not realized. It is shown that at small w the magnitude mz * can be as a criterion of magnetization reversal. I.e., if mz * <0, the magnetization reversal would happen with 100 percent probability. The results can be used in various areas of superconducting spintronics, in particular, to create a memory element based on the Josephson $ {\varphi_0} $ junction