  Using deep (11.2hr) VLT/MUSE data from the MEGAFLOW survey, we report the
first detection of extended MgII emission from a galaxy's halo that is probed
by a quasar sightline. The MgII $\lambda\lambda$ 2796,2803 emission around the
$z = 0.702$ galaxy ($\log(M_*/\mathrm{M_\odot}) = 10.05^{+0.15}_{-0.11}$) is
detected out to $\approx$25 kpc from the central galaxy and covers
$1.0\times10^3$ kpc$^2$ above a surface brightness of $14\times10^{-19}
\mathrm{erg} \mathrm{s}^{-1} \mathrm{cm}^{-2}\,\mathrm{arcsec}^{-2}$ ($2
\sigma$; integrated over 1200 km s$^{-1}$ =19A and averaged over $1.5
\;\mathrm{arcsec}^2$). The MgII emission around this highly inclined galaxy
($\simeq$75 deg) is strongest along the galaxy's projected minor axis,
consistent with the MgII gas having been ejected from the galaxy into a
bi-conical structure. The quasar sightline, which is aligned with the galaxy's
minor axis, shows strong MgII $\lambda$2796 absorption (EW$_0$ = 1.8A) at an
impact parameter of 39kpc from the galaxy. Comparing the kinematics of both the
emission and the absorption - probed with VLT/UVES -, to the expectation from a
simple toy model of a bi-conical outflow, we find good consistency when
assuming a relatively slow outflow ($v_\mathrm{out}=
130\;\mathrm{km}\,\mathrm{s}^{-1}$). We investigate potential origins of the
extended MgII emission using simple toy models. With continuum scattering
models we encounter serious difficulties in explaining the luminosity of the
MgII halo and in reconciling density estimates from emission and absorption.
Instead, we find that shocks might be a more viable source to power the
extended MgII (and non-resonant [OII]) emission.
