Summary: For studying the details of the physical processes concerning space-time relations of signal exchanges in moving inertial-systems, it is purposeful to make at first a short exposition of the kinematics of electromagnetic wave propagation from a moving source to a stationary or moving field point in the free unbounded space. An introductory analysis on the kinematics of wave propagation from a source to an observer in a moving inertial system follows thereafter, primarily for elucidating the natural causality of the source and the observer remaining centered at the common midpoint of the radiating waves, without undergoing any relative drift. Special emphasis is then put to study the space-time relations of wave propagation from a source to an observer in the moving inertial system. The use of the emitting and receiving signal-cones in the moving system, with their common plane-cut, provides all the details with convincing insights concerning the causality and effect, both in the absolute space and in the Lorentz-space. The essential findings are elucidated with application to numerical examples and corresponding illustrations.