According to the current understanding of physics, two galaxies moving apart with a redshift (z) greater than 1.4, such that their relative recessional velocity exceeds the speed of light, would not be able to have a shared inertial frame of reference.
The concept of a shared inertial frame of reference implies that two objects are in a state of relative rest or uniform motion with respect to each other, without any acceleration or external forces acting upon them. In such a frame, the laws of physics, including the principles of special relativity, hold true.
When the recessional velocity between two objects exceeds the speed of light, it means that the distance between them is increasing faster than light can traverse that distance. This expansion of space is a feature of the expanding universe and is described by the cosmological redshift.
As objects recede from each other at speeds greater than the speed of light, the light they emit towards each other cannot bridge the increasing gap between them. Therefore, they cannot establish a direct cause-and-effect relationship or communicate with each other through electromagnetic signals.
It's important to note that the recessional velocity between galaxies is not due to the motion of the galaxies themselves but rather the expansion of the space between them. This expansion is governed by the dynamics of the universe on cosmological scales, described by general relativity and supported by observational evidence, such as the redshift of light from distant galaxies.
In summary, if two galaxies are moving apart at velocities greater than the speed of light due to the expansion of space, they would not be able to have a shared inertial frame of reference, and direct communication or a direct cause-and-effect relationship between them would not be possible.