PbS molecular clusters and quantum dots (QDs) have been formed by heat treatment in fluorophosphate glasses of the Na2O3–Р2O5–Ga2O3–ALF3–ZnO(S)–PbF2 system, and their spectral-luminescence characteristics have been investigated. It is experimentally shown that the transition from molecular clusters to QDs is accompanied by a stepwise change in the spectrum and luminescence quantum yield. Molecular PbS clusters luminesce in the visible spectral range (1.5–3.5 eV) and QDs luminesce in the IR region (0.6–1.4 eV). The luminescence of molecular PbS clusters is characterized by low quantum yield, which decreases from 10 to 1% with an increase in excitation energy. An increase in nanoparticle size leads to a decrease in the Stokes shift from 80 to 50 meV. The QD luminescence spectrum contains two bands, which are due to transitions from two lower excited states.