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.
All of these sizable deviations in the h decays are due to (i) large
scharm-stop mixing and large scharm/stop involved trilinear couplings
$T_{U23}, T_{U32}, T_{U33}$, (ii) large sstrange-sbottom mixing and large
sstrange/sbottom involved trilinear couplings $T_{D23}, T_{D32}, T_{D33}$
and (iii) large bottom Yukawa coupling $Y_b$ for large $\tan\beta$ and
large top Yukawa coupling $Y_t$.
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).