In this paper, a one-dimensional elastic–electronic deformation problem under the influence of the magnetic field will be inspected. Furthermore, the non-homogeneous (functionally graded) properties of semiconductor materials in the context of the photo-thermoelasticity theory will be studied. The hyperbolic two-temperature theory is taken into consideration during the photo-excited transport process. The interactions among the thermal, plasma, and elastic waves are analytically obtained when the optical and elastic parameters of the semiconductor medium are utilized as a function in the distance. The governing equations are formed using the Laplace transform technique to identify the analytical solutions of the key physical field distributions in the Laplace domain. Some thermal load, mechanical force, and plasma recombination conditions can be implemented at the free surface of the semiconductor medium. To illustrate the importance and effectiveness of the obtained results, the complete solutions of the main physical quantities in the space–time domain are identified using a numerical technique based on the inverse of the Laplace transform. Moreover, this work demonstrates the main physical field quantities that will be graphically represented and theoretically discussed. Many comparisons are made according to the influence of some parameters when thermal memories are taken into consideration.