  The three-dimensional Schr\"odinger equation with a position-dependent
(effective) mass is studied in the framework of Supersymmetrical (SUSY) Quantum
Mechanics. The general solution of SUSY intertwining relations with first order
supercharges is obtained without any preliminary constraints. Several forms of
coefficient functions of the supercharges are investigated and analytical
expressions for the mass function and partner potentials are found. As usual
for SUSY Quantum Mechanics with nonsingular superpotentials, the spectra of
intertwined Hamiltonians coincide up to zero modes of supercharges, and the
corresponding wave functions are connected by intertwining relations. All
models are partially integrable by construction: each of them has at least one
second order symmetry operator.
