  A search for a charged Higgs boson 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 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 H$^\pm$ mass of 300 GeV to 0.019 pb for a mass of 700 GeV. These are the
first limits on H$^\pm$ production in the H$^\pm$ $\to$ HW$^\pm$ decay channel
at the LHC.
