  On using the known equivalence between the presence of a position-dependent
mass (PDM) in the Schr\"odinger equation and a deformation of the canonical
commutation relations, a method based on deformed shape invariance has recently
been devised for generating pairs of potential and PDM for which the
Schr\"odinger equation is exactly solvable. This approach has provided the
bound-state energy spectrum, as well as the ground-state and the first few
excited-state wavefunctions. The general wavefunctions have however remained
unknown in explicit form because for their determination one would need the
solutions of a rather tricky differential-difference equation. Here we show
that solving this equation may be avoided by combining the deformed shape
invariance technique with the point canonical transformation method in a novel
way. It consists in employing our previous knowledge of the PDM problem energy
spectrum to construct a constant-mass Schr\"odinger equation with similar
characteristics and in deducing the PDM wavefunctions from the known
constant-mass ones. Finally, the equivalence of the wavefunctions coming from
both approaches is checked.
