  First order integrals of motion for Schr\"odinger equations with position
dependent masses are classified. Seventeen classes of such equations with
non-equivalent symmetries are specified. They include integrable,
superintegrable and maximally superintegrable systems. Among them is a system
invariant with respect to the Lie algebra of Lorentz group and a system whose
integrals of motion form algebra so(4). Three of the obtained systems are
solved exactly.
