A search for a charged Higgs boson ${\mathrm{\tilde{H}^{\pm}}}$ decaying into a heavy neutral Higgs boson H and a W boson is presented. The analysis targets the H decay into a pair of tau leptons with at least one of them decaying hadronically and with an additional electron or muon present in the event. The search is based on proton-proton collision data recorded by the CMS experiment during 2016-2018 at $\sqrt{s} =$ 13 TeV, corresponding to an integrated luminosity of 138 fb$^{-1}$. The data are consistent with standard model background expectations. Upper limits at 95% confidence level are set on the product of the cross section and branching fraction for an ${\mathrm{\tilde{H}^{\pm}}}$ in the mass range of 300-700 GeV, assuming an H with a mass of 200 GeV. The observed limits range from 0.085 pb for an ${\mathrm{\tilde{H}^{\pm}}}$ mass of 300 GeV to 0.019 pb for a mass of 700 GeV. These are the first limits on ${\mathrm{\tilde{H}^{\pm}}}$ production in the ${\mathrm{\tilde{H}^{\pm}}} \to \mathrm{H} \mathrm{W^{\pm}}$ decay channel at the LHC.

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