  Maximal kinematical invariance groups of $2d$ Schr\"odinger equation with a
position dependent mass and arbitrary potential are classified. It is
demonstrated that there exist seven classes of such equations possessing
non-equivalent continuous symmetry group. Three of these classes include
arbitrary functions while the remaining ones are defined up to arbitrary
parameters. In particular, for the case of a constant mass the class missing in
the Boyer classification (Boyer C P 1974 Helv. Phys. Acta{\bf 47}, 450) is
indicated. A constructive test of (non)equivalence of a PDM system to a
constant mass system is proposed.
