The most precise test of the post-Newtonian gamma parameter in the solar system has been achieved in measurement of the frequency shift of radio waves to and from the Cassini spacecraft as they passed near the Sun. The test relies upon the JPL model of radiowave propagation that includes, but does not explicitly parametrize, the impact of the non-stationary component of the gravitational field of the Sun, generated by its barycentric orbital motion, on the Shapiro delay. This non-stationary gravitational field of the Sun is associated with the Lorentz transformation of the metric tensor and the affine connection from the heliocentric to the barycentric frame of the solar system and can be treated as gravimagnetic field. The gravimagnetic field perturbs the propagation of a radio wave and contributes to its frequency shift at the level up to 4 10^{-13} that may affect the precise measurement of the parameter gamma in the Cassini experiment to about one part in 10,000. Our analysis suggests that the translational gravimagnetic field of the Sun can be extracted from the Cassini data, and its effect is separable from the space curvature characterized by the parameter gamma
