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The measured branching fractions of $B$-mesons into leptonic final statesderived by the LHCb collaboration hint towards the breakdown of lepton flavouruniversality. In this work we take at face value the so-called $R_{D^{(*)}}$observables that are defined as the ratios of neutral $B$-meson charged-currentdecays into a charged $D$-meson, a charged lepton and a neutrino final state inthe tau and muon channels. A well-studied and simple solution to this chargedcurrent anomaly is to introduce a scalar leptoquark $S_1$ that couples to thesecond and third generation of fermions. We investigate how $S_1$ can alsoserve as a mediator between the Standard Model and a dark sector. We study thisscenario in detail and estimate the constraints arising from collider searchesfor leptoquarks, collider searches for missing energy signals, direct detectionexperiments and the dark matter relic abundance. We stress that the productionof a pair of leptoquarks that decays into different final states (i.e. thecommonly called "mixed" channels) provides critical information for identifyingthe underlying dynamics, and we exemplify this by studying the $t \tau b \nu$and the resonant $S_1$ plus missing energy channels. We find that directdetection data provides non-negligible constraints on the leptoquark couplingto the dark sector, which in turn affects the relic abundance. We also showthat the correct relic abundance can not only arise via standard freeze-out,but also through conversion-driven freeze-out. We illustrate the richphenomenology of the model with a few selected benchmark points, providing abroad stroke of the interesting connection between lepton flavour violation anddark matter.

Leptoquark manoeuvres in the dark: a simultaneous solution of the dark matter problem and the $R_{D^{(*)}}$ anomalies