We report the detection, made using ALMA, of the 92 GHz continuum and hydrogen recombination lines (HRLs) H40$alpha$, H42$alpha$, and H50$beta$ emission toward the ionized wind associated with the high-mass young stellar object G345.4938+01.4677. This is the luminous central dominating source located in the massive and dense molecular clump associated with IRAS 16562$-$3959. The HRLs exhibit Voigt profiles, a strong signature of Stark broadening. We successfully reproduce the observed continuum and HRLs simultaneously using a simple model of a slow ionized wind in local thermodynamic equilibrium, with no need a high-velocity component. The Lorentzian line wings imply electron densities of $5times10^7$ cm$^{-3}$ on average. In addition, we detect SO and SO$_2$ emission arising from a compact ($sim3000$ AU) molecular core associated with the central young star. The molecular core exhibits a velocity gradient perpendicular to the jet-axis, which we interpret as evidence of rotation. The set of observations toward G345.4938+01.4677 are consistent with it being a young high-mass star associated with a slow photo-ionized wind.
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