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Using very deep observations (27 h) of the <jats:italic>Hubble <\/jats:italic>Deep Field South with the Multi Unit Spectroscopic Explorer (MUSE) instrument, we identify signatures of an outflow in both emission and absorption from a spatially resolved galaxy at <jats:italic>z<\/jats:italic> = 1.29 with a stellar mass <jats:italic>M<\/jats:italic><jats:sub><jats:italic>\u22c6<\/jats:italic><\/jats:sub> = 8 \u00d7 10<jats:sup>9<\/jats:sup><jats:italic>M<\/jats:italic><jats:sub>\u2299<\/jats:sub>, star formation rate <jats:italic>SFR<\/jats:italic> = 77<jats:sup>+40<\/jats:sup><jats:sub>-25 <\/jats:sub><jats:italic>M<\/jats:italic><jats:sub>\u2299<\/jats:sub> yr<jats:sup>-1<\/jats:sup>, and star formation rate surface brightness \u03a3<jats:sub>SFR<\/jats:sub> = 1.6<jats:italic>M<\/jats:italic><jats:sub>\u2299<\/jats:sub> kpc<jats:sup>-2<\/jats:sup> within the [Oii]\u2009<jats:italic>\u03bb\u03bb<\/jats:italic>3727,3729 half-light radius <jats:italic>R<\/jats:italic><jats:sub>1\/2,  [OII]<\/jats:sub> =\u20092.76 \u00b1 0.17 kpc. From a component of the strong resonant Mg\u2009<jats:sc>ii <\/jats:sc>and Fe\u2009<jats:sc>ii <\/jats:sc>absorptions at \u2212350 km s<jats:sup>-1<\/jats:sup>, we infer a mass outflow rate that is comparable to the star formation rate. We detect non-resonant Fe\u2009<jats:sc>ii<\/jats:sc>* emission, at <jats:italic>\u03bb<\/jats:italic>2365, <jats:italic>\u03bb<\/jats:italic>2396, <jats:italic>\u03bb<\/jats:italic>2612, and <jats:italic>\u03bb<\/jats:italic>2626, at 1.2\u22122.4\u22121.5\u22122.7 \u00d7 10<jats:sup>-18<\/jats:sup> erg s<jats:sup>-1<\/jats:sup> cm<jats:sup>-2<\/jats:sup> respectively. The flux ratios are consistent with the expectations for optically thick gas. By combining the four non-resonant Fe\u2009<jats:sc>ii<\/jats:sc>* emission lines, we spatially map the Fe\u2009<jats:sc>ii<\/jats:sc>* emission from an individual galaxy for the first time. The Fe\u2009<jats:sc>ii<\/jats:sc>* emission has an elliptical morphology that is roughly aligned with the galaxy minor kinematic axis, and its integrated half-light radius, <jats:italic>R<\/jats:italic><jats:sub>1\/2, Fe <jats:sc>ii<\/jats:sc> \u2217<\/jats:sub> =4.1 \u00b1 0.4 kpc, is 70% larger than the stellar continuum (<jats:italic>R<\/jats:italic><jats:sub>1\/2,<jats:italic>\u22c6<\/jats:italic><\/jats:sub> \u22432.34 \u00b1 0.17) or the [Oii] nebular line. Moreover, the Fe\u2009<jats:sc>ii<\/jats:sc>* emission shows a blue wing extending up to \u2212400 km\u2009s<jats:sup>-1<\/jats:sup>, which is more pronounced along the galaxy minor kinematic axis and reveals a C-shaped pattern in a <jats:italic>p<\/jats:italic>\u2212<jats:italic>v<\/jats:italic> diagram along that axis. 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