  In recent years, evidence for lepton flavour universality violation beyond
the Standard Model has been accumulated. In this context, a singly charged
$SU(2)_L$ singlet scalar ($\phi^\pm$) is very interesting, as it can only have
flavour off-diagonal couplings to neutrinos and charged leptons, therefore
necessarily violating lepton flavour (universality). In fact, it gives a
(necessarily constructive) tree-level effect in $\ell\to\ell^\prime\nu\nu$
processes, while contributing to charged lepton flavour violating only at the
loop-level. Therefore, it can provide a common explanation of the hints for new
physics in
  $\tau\to\mu\nu\nu/\tau(\mu)\to e\nu\nu$ and of the Cabibbo Angle Anomaly.
Such an explanation predicts ${\rm Br }[\tau\to e\gamma]$ to be of the order of
a few times $10^{-11}$ while ${ \rm Br}[\tau\to e\mu\mu]$ can be of the order
of $10^{-9}$ for order one couplings and therefore in the reach of forthcoming
experiments. Furthermore, we derive a {novel} coupling-independent lower limit
on the scalar mass of $\approx 200\,$GeV by recasting LHC slepton searches. In
the scenario preferred by low energy precision data, the lower limit is even
strengthened to $\approx300\,$GeV, showing the complementary between LHC
searches and flavour observables. Furthermore, we point out that this model can
be tested by reinterpreting DM mono-photon searches at future $e^+e^-$
colliders.

High Energy Physics - Phenomenology;High Energy Physics - Experiment;Nuclear Experiment;Nuclear Theory