We construct an extension of the Standard Model with a scalar leptoquark $ϕ\sim (3,1,-\tfrac13)$ and the discrete flavour symmetry $G_f=D_{17}\times Z_{17}$ to explain anomalies observed in charged-current semi-leptonic $B$ meson decays and in the muon anomalous magnetic moment, together with the charged fermion masses and quark mixing. The symmetry $Z_{17}^{\rm diag}$, contained in $G_f$, remains preserved by the leptoquark couplings, at leading order, and efficiently suppresses couplings of the leptoquark to the first generation of quarks and/or electrons, thus avoiding many stringent experimental bounds. The strongest constraints on the parameter space are imposed by the radiative charged lepton flavour violating decays $τ\toμγ$ and $μ\to eγ$. A detailed analytical and numerical study demonstrates the feasibility to simultaneously explain the data on the lepton flavour universality ratios $R(D)$ and $R(D^\star)$ and the muon anomalous magnetic moment, while passing the experimental bounds from all other considered flavour observables.

71 pages + appendices, 27 figures Matches version accepted for publication in Physical Review D