Purpose <p>This work aims at enhancing a suitable framework for generalized thermoelastic heat transfer. On behalf of an innovative theory of generalized thermoelasticity confined to the Moore–Gibson–Thompson equation, the plane waves in an orthotropic thermoelastic material reinforced with fibers have been examined.</p> Methods <p>The harmonic representation of waves is utilized to determine the solution to the problem. Based on the solution, it is revealed that three coupled waves traveling at distinct speeds through the medium.</p> Results <p>The impact of Hall current in the presence of an external magnetic field on the propagating waves is also explored. The mathematical representation of energy ratios is derived for the reflected waves. The consequence of two temperature parameter, Hall parameter and the MGT theory are additionally recognized by assessing the amplitude ratios among various reflected waves versus the angle of incidence.</p> Conclusion <p>The study delves into the reflection phenomenon of these waves from thermally insulated stress-free surface, resulting in a system of three non-homogeneous equations describing the amplitude ratios of reflected waves. Furthermore, the study successfully replicates previously published results in scenarios where Hall current, two temperature parameter and fiber-reinforcement are absent. The primary motivation is to expand upon generalized thermoelastic theories using the Moore–Gibson–Thompson equation, particularly in the context of fiber-reinforced orthotropic materials. The significance of this study lies in its ability to provide a deeper understanding of wave behavior in complex environments, offering practical insights for materials used in advanced technological fields.</p>