classical electrodynamics - Interaction between charged particles as seen from two inertial frames of references

Let us consider two charged particles travelling at a uniform velocity, V, as seen from a frame of reference A . Now let us consider a frame of reference, B, which is also travelling at a uniform velocity V with respect to A. Now the interaction of the two charged particles as seen from A would give rise to EM waves. (Initially, I thought that acceleration of charged particles is necessary for EM waves, but an answer to my last question shows a system of equations for this interaction giving an EM wave). Now let us consider the interaction of the two particles as seen from B. As seen from B, this interaction would be an electrostatic interaction. But the EM waves once generated will propagate everywhere in space and hence should also be detected in the reference frame B. And at the same time there doesn't seem to be any way in which the waves can evade the reference frame B. Although I admit I am unaware of the way field transformation takes place, I still guess that if a field is changing in a wave-like manner in one frame of reference then the field to which it gets transformed must also change in such a manner. So, what exactly happens in such a scenario ?