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Motivated by the measurements of $b\to s\ell^+\ell^-$ transitions, including$R(K)$ and $R(K^*)$, we examine lepton flavour (universality) violation in $B$decays and its connections to $\mu\to e\gamma$ in generic leptoquark models.Considering all 10 representations of scalar and vector leptoquarks under theStandard Model gauge group we compute the tree-level matching for semileptonic$b$-quark operators as well as their loop effects in$\ell\to\ell^\prime\gamma$. In our phenomenological analysis we correlate$R(K)$, $R(K^*)$ and the other $b\to s\mu^+\mu^-$ data to $\mu\to e\gamma$ and$b\to s\mu e$ transitions for the three leptoquark representations thatgenerate left-handed currents in $b\to s\ell^+\ell^-$ transitions and,therefore, provide a good fit to data. We find that while new physicscontributions to muons are required by the global fit, also couplings toelectrons can be sizeable without violating the stringent bounds from $\mu\toe\gamma$. In fact, if the effect in electrons in $b\to s\ell^+\ell^-$ hasopposite sign than the effect in muons the bound from $\mu\to e\gamma$ canalways be avoided. However, unavoidable effects in $b\to s\mu e$ transitions(i.e. $B_s\to\mu e$, $B\to K\mu e$, etc.) appear which are within the reach ofLHCb and BELLE II.

Correlating Lepton Flavour (Universality) Violation in $B$ Decays with $\mu\to e\gamma$ using Leptoquarks