  Context. Extragalactic Planetary Nebulae (PNe) are useful distance indicators
and are often used to trace the dark-matter content in external galaxies. At
the same time, PNe can also be used as probes of their host galaxy stellar
populations and to help understanding the later stages of stellar evolution.
Previous works have indicated that specific number of PNe per stellar
luminosity can vary across different galaxies and as a function of
stellar-population properties, for instance increasing with decreasing stellar
metallicity.
  Aims. In this study we further explore the importance of stellar metallicity
in driving the properties of the PNe population in early-type galaxies, using
three edge-on galaxies in the Fornax cluster offering a clear view into their
predominantly metal-rich and metal-poor regions near the equatorial plane or
both below and above it, respectively .
  Methods. Using VLT-MUSE integral-field observations and dedicated PNe
detection procedures, we construct the PNe luminosity function and compute the
luminosity-specific number of PNe alpha in both in- and off-plane regions of
our edge-on systems.
  Results. Comparing these alpha values with metallicity measurements also
based on the same MUSE data, we find no evidence for an increase in the
specific abundance of PNe when transitioning between metal-rich and metal-poor
regions.
  Conclusions. Our analysis highlights the importance of ensuring spatial
consistency to avoid misleading results when investigating the link between PNe
and their parent stellar populations and suggest that in passively-evolving
systems variations in the specific number of PNe may pertain to rather extreme
metallicity regimes found either in the innermost or outermost regions of
galaxies.
