  Recently reported [Eur. Phys. J. C., ${\bf 77}$, 549 (2017)]
gravitoelectromagnetic equations of Ummarino and Gallerati (UG) in their
linearized version of General Relativity (GR) are shown to match with (a) our
previously reported special relativistic Maxwellian Gravity equations in the
non-relativistic limit and with (b) the non-relativistic equations derived
here, when the speed of gravity $c_g$ (an undetermined parameter of the theory
here) is set equal to $c$ (the speed of light in vacuum). Seen in the light of
our new results, the UG equations satisfy the Correspondence Principle (cp),
while many other versions of linearized GR equations that are being (or may be)
used to interpret the experimental data defy the cp. Such new findings assume
significance and relevance in the contexts of recent detection of gravitational
waves and the gravitomagnetic field of the spinning earth and their
interpretations. Being well-founded and self-consistent, the equations may be
of interest and useful to researchers exploring the phenomenology of
gravitomagnetism, gravitational waves and the novel interplay of gravity with
different states of matter in flat space-time like UG's interesting work on
superconductors in weak gravitational fields.
