One of the important topics in nanomagnetics concerns the use of spin valves for generation of the microwave GHz-frequency oscillations. The power output of an individual spin valve can be increased by synchronization of several devices, which was successfully confirmed experimentally. To achieve such synchronization, the values of applied magnetic field and injected spin current should be properly adjusted. We made numerical simulations for a linear chain of macrospins aimed to determine the parameters required for an efficient propagation of magnetization oscillations through a sandwich structure of ten thin ferromagnetic layers separated by non-magnetic spacers. The individual layers were assumed coupled only by spin-polarized current flowing through the system. We report the presence of considerable areas in parameter space, for which magnetic motion in a macrospin chain becomes synchronized after a short period of time, which may have significant importance for the possible device applications.