  In a previous work we showcased the factorization method to find the
symmetries of superintegrable systems with spherical separability in flat
spaces. Here we analyze the same problem, but in constant curvature spaces
along the examples of curved Kepler-Coulomb and Harmonic Oscillator systems. We
also show how this procedure can also be directly extended to the curved
Smorodinsky-Winternitz (SW) and Evans systems.
