Abstract <p> We construct and study transport solutions of the biquaternion wave equation, which is a biquaternion generalization of the Dirac and Maxwell equations. These equations describe the electromagnetic fields of electromagnetic and electro-gravimagnetic wave sources moving in a fixed direction with a constant speed that is less than the speed of wave propagation in an electromagnetic medium (speed of light). We construct fundamental and generalized transport solutions describing fields of moving objects at subluminal speeds. Using the Fourier transform of distributions, we construct a biquaternion Green function (bifunction) in a moving coordinate system. This function describes the field generated by a moving point source on the <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(z\)</EquationSource> </InlineEquation>-axis. We find the energy density and the Poynting vector of this field. The influence of the speed of motion on the field characteristics is studied. </p>