between two crystals and the Dutra’s and Almeida’s [14] reliability test. Even the form of the potential and/or the form of the position dependent mass may have their say in the process, so to speak. Such ambiguity in the non-uniqueness representation of the position-dependent mass Schr¨ odinger Hamiltonian should be attributed to the lack of the Galilean invariance (cf., e.g., ref.[33] for more details on the issue). To the best of our knowledge, such a study has not been considered else- where, not only within the Hermitian PDM-Hamiltonians’ settings, but neither within the complex non-Hermitian settings. A gap that remains interesting and merits exploration/attention. . 9