  The longstanding muon $(g-2)$ anomaly, as well as the persistent hints of
lepton flavor universality violation in $B$-meson decays, could be signaling
new physics beyond the Standard Model (SM). A minimal $R$-parity-violating
supersymmetric framework with light third-generation sfermions (dubbed as
'RPV3') provides a compelling solution to these flavor anomalies, while
simultaneously addressing other pressing issues of the SM. We propose a new
RPV3 scenario for the solution of the muon $(g-2)$ anomaly, which leads to an
interesting LHC signal of $\mu^+\mu^-\tau^+\tau^-$ final state. We analyze the
Run-2 LHC multilepton data to derive stringent constraints on the sneutrino
mass and the relevant RPV coupling in this scenario. We then propose dedicated
selection strategies to improve the bound even with the existing dataset. We
also show that the high-luminosity LHC will completely cover the remaining muon
$(g-2)$-preferred parameter space, thus providing a robust, independent test of
the muon $(g-2)$ anomaly.
