A search for a charged Higgs boson $\mathrm{H^{\pm}}$ decaying into a heavy neutral Higgs boson $\mathrm{H}$ and a $\mathrm{W}$ boson is presented. The analysis targets the $\mathrm{H}$ boson 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~\mathrm{TeV}, corresponding to an integrated luminosity of 138~\mathrm{fb}^{-1}. The observed data are consistent with standard model expectations. Upper limits at $95\%$ confidence level are set on the product of the cross section and branching fraction for an $\mathrm{H^{\pm}}$ in the mass range of 300 to 700~\mathrm{GeV}, assuming an $\mathrm{H}$ with a mass of 200~\mathrm{GeV}. The observed limit ranges from 0.080~\mathrm{pb} at 300~\mathrm{GeV} to 0.013~\mathrm{pb} at 700~\mathrm{GeV}. These are the first limits on this process at the LHC.

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