  We study the CP-even neutral Higgs boson decays $h \to c \bar{c}, b \bar{b},
b \bar{s}, \gamma \gamma, g g$ in the Minimal Supersymmetric Standard Model
(MSSM) with general quark flavor violation (QFV), identifying the h as the
Higgs boson with a mass of 125 GeV. We compute the widths of the h decays to $c
\bar c, b \bar b, b \bar s (s \bar b)$ at full one-loop level. For the
loop-induced h decays to photon photon and gluon gluon we compute the widths at
NLO QCD level. {\it For the first time}, we perform a systematic MSSM parameter
scan including Supersymmetric (SUSY) QFV parameters respecting all the relevant
constraints, i.e. theoretical constraints from vacuum stability conditions and
experimental constraints, such as those from K- and B-meson data, electroweak
precision data, and the 125 GeV Higgs boson data from recent LHC experiments,
as well as the limits on SUSY particle masses from the LHC experiment. We also
take into account the expected SUSY particle mass limits from the future HL-LHC
experiment in our analysis. {\it In strong contrast to} the usual studies in
the MSSM with quark flavor conservation, we find that the deviations of these
MSSM decay widths from the Standard Model (SM) values can be quite sizable and
that there are significant correlations among these deviations. Future lepton
colliders such as ILC, CLIC, CEPC, FCC-ee and MuC can observe such sizable
deviations from the SM at high signal significance {\it even after} the failure
of SUSY particle discovery at the HL-LHC. In case the deviation pattern shown
here is really observed at the lepton colliders, then it would strongly suggest
the discovery of QFV SUSY (the MSSM with general QFV).
