Binary population synthesis predict a population of helium-core white dwarfs (He WDs) in cataclysmic variables (CVs) that is not observed in the available sample of CVs. An independent test on the fraction of He WDs in close WD binaries can be provided by analysing post-common-envelope binaries (PCEBs) consisting of a WD and a main-sequence companion. Here we present a sample of 63 PCEBs and find the fraction of He WD primaries considerably exceeding the He WD fraction observed in CVs. However, taking into account the time the PCEBs need to become CVs, i.e. excluding systems with CV formation times exceeding the age of tha Galaxy, and requesting stable mass transfer, we find the fraction of He WD primaries in agreement with the current CV sample.