The present paper proposes an advancement beyond the recent mathematical formulation [Cherroud O and Yahiaoui S-A 2023 Eur. Phys. J. Plus. 138 534], by extending their approach to the evaluation of off-diagonal matrix elements 〈xˆmpˆl〉n,n′J,J′ for the rotation-vibration Morse oscillators. Calculations are conducted within the framework of phase-space quantum mechanics, considering (r → r eq). This methodology facilitates the derivation of analytical expressions for 〈xˆs〉n,n′J,J′ and 〈pˆs〉n,n′J,J′ matrix elements, where s = 1, 2, …. This approach enables the evaluation of both diagonal ( n=n′,J=J′≠0 ) and off-diagonal ( n≠n′,J=J′≠0 ) matrix elements through a more explicit and compact analytic formula, applicable for cases where J≠J′ as well as for scenarios involving non-rotating effects J=J′=0 .