  In a recent paper by Jafarov, Nagiyev, Oste and Van der Jeugt (2020 {\sl J.\
Phys.\ A} {\bf 53} 485301), a confined model of the non-relativistic quantum
harmonic oscillator, where the effective mass and the angular frequency are
dependent on the position, was constructed and it was shown that the
confinement parameter gets quantized. By using a point canonical transformation
starting from the constant-mass Schr\"odinger equation for the Rosen-Morse II
potential, it is shown here that similar results can be easily obtained without
quantizing the confinement parameter. In addition, an extension to a confined
shifted harmonic oscillator directly follows from the same point canonical
transformation.
