  We extend the abundance matching technique (AMT) to infer the
satellite-subhalo and central-halo mass relations (MRs) of galaxies, as well as
the corresponding satellite conditional mass functions (CMFs). We use the
observed galaxy stellar mass function (GSMF) decomposed into centrals and
satellites and the LCDM halo/subhalo mass functions as inputs. We explore the
effects of defining the subhalo mass at the time of accretion (m_acc) vs. at
the time of observation (m_obs). We test the standard assumption that centrals
and satellites follow the same MRs, showing that this assumption leads to
predictions in disagreement with observations, specially for m_obs. Instead,
when the satellite-subhalo MRs are constrained following our AMT, they are
always different from the central-halo MR: the smaller the stellar mass (Ms),
the less massive is the subhalo of satellites as compared to the halo of
centrals of the same Ms. On average, for Ms<2x10^11Msol, the dark mass of
satellites decreased by 60-65% with respect to their masses at accretion time.
The resulting MRs for both definitions of subhalo mass yield satellite CMFs in
agreement with observations. Also, when these MRs are used in a HOD model, the
predicted correlation functions agree with observations. We show that the use
of m_obs leads to less uncertain MRs than m_acc, and discuss implications of
the obtained satellite-subhalo MR. For example, we show that the tension
between abundance and dynamics of MW satellites in LCDM gives if the slope of
the GSMF faint-end slope upturns to -1.6.
