  In this study, we investigate the anomalous magnetic moment of the muon
$(g_\mu-2)$ as reported by Fermilab (FNAL), along with the recent measurement
of the $W$-boson mass by the CDF-II collaboration. Both findings show
significant deviations from the predictions of the Standard Model (SM), hinting
at the possibility of new physics. Our focus is on the Type III
two-Higgs-doublet model (2HDM), wherein both Higgs doublets couple with all
fermions, leading to the induction of flavour-changing neutral currents (FCNCs)
at the tree level. Within this framework, we investigate a
lepton-flavour-violating (LFV) scenario, aiming to explain both observed
anomalies, while satisfying the up-to-date theoretical and experimental
constraints.
