  In this letter, we propose a new method for measuring the Sachs form factors
ratio ($R =\mu_p G_E/G_M$) based on the transfer of polarization from the
initial proton to the final electron in the elastic $e \vec p \to \vec e p$
process, in the case when the axes of quantization of spins of the target
proton at rest and of the scattered electron are parallel, i.e., when an
electron is scattered in the direction of the spin quantization axis of the
proton target. To do this, in the kinematics of the SANE collaboration
experiment (2020) on measuring double spin asymmetry in the $\vec e\vec p \to e
p$ process, using Kelly (2004) and Qattan (2015) parametrizations, a numerical
analysis was carried out of the dependence of the longitudinal polarization
degree of the scattered electron on the square of the momentum transferred to
the proton, as well as on the scattering angles of the electron and proton. It
is established that the difference in the longitudinal polarization degree of
the final electron in the case of conservation and violation of scaling of the
Sachs form factors can reach 70%. This fact can be used to set up polarization
experiments of a new type to measure the ratio $R$.
