We study the lighter CP-even neutral Higgs boson decays $h \to c \bar{c}, b \bar{b},
\gamma \gamma, g g$ 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 these $h$ decays and the width ratios at NLO level
focusing on their deviations from the standard model (SM) predictions.
From a systematic MSSM parameter scan respecting all the relevant theoretical
and experimental constraints, such as those from K- and B-meson data and
the Supersymmetric (SUSY) particle mass limits from the LHC experiments,
we find that the deviations of these MSSM decay width ratios from their
SM values can be quite sizable in strong contrast to the usual studies
in the MSSM with Minimal Flavor Violation (MFV).
We point out that the
experimental measurement uncertainties as well as the MSSM prediction uncertainties
tend to cancel out significantly in the width ratios, making the measurement
of these width ratios a very sensitive probe of virtual SUSY loop effects
in these $h$ decays at future lepton colliders such as ILC, CLIC, CEPC, FCC-ee
and muon-collider (MuC).
We show that the deviations of the width ratios
can be significantly enhanced compared with that of a single width; e.g. the
deviation of the decay width ratio $\Gamma(h \to b \bar b)/\Gamma(h \to c \bar c)$
from the SM value can exceed +100% and that of $\Gamma(h \to \gamma \gamma)/\Gamma(h \to g g)$
from the SM value can be as large as about +8%.
Moreover, we find that future lepton colliders such as ILC, CLIC, CEPC, FCC-ee
and MuC can observe such sizable deviations of the width ratios from the SM
at high signal significance 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).