<p>This work provides an exact analytical solution for a particle with position-dependent mass in a generalized Morse-type potential. Using a Hulthén-type mass distribution and the von Roos symmetrization scheme, the model captures both molecular short-range effects and operator-ordering ambiguities. The problem is elegantly solved using supersymmetric quantum mechanics (SUSYQM), yielding closed-form energy spectra and bound-state wavefunctions expressed in terms of hypergeometric functions and Jacobi polynomials. The role of ambiguity parameters is clarified, with precise conditions ensuring the existence of bound states and the preservation of supersymmetry. Beyond its theoretical rigor, the framework offers a versatile tool for studying realistic systems such as heterostructures and molecules, and can be extended to other mass distributions and potentials.</p>