  Molecular outflows contributing to the matter cycle of star forming galaxies
are now observed in small and large systems at low and high redshift. Their
physical origin is still unclear. In most theoretical studies only warm
ionised/neutral and hot gas outflowing from the interstellar medium is
generated by star formation. We investigate an in-situ H$_2$ formation scenario
in the outflow using high-resolution simulations, including non-equilibrium
chemistry and self-gravity, of turbulent, warm, and atomic clouds with
densities 0.1, 0.5 and $1\,\mathrm{cm}^{-3}$ exposed to a magnetised hot wind.
For cloud densities $\gtrsim 0.5\,\mathrm{cm}^{-3}$ a magnetised wind triggers
H$_2$ formation before cloud dispersal. Up to 3 per cent of the initial cloud
mass can become molecular on $\sim 10\,\mathrm{Myr}$ time scales. The effect is
stronger for winds with perpendicular $B$-fields and intermediate density
clouds ($n_\mathrm{c}\sim 0.5\,\mathrm{cm}^{-3}$). Here H$_2$ formation can be
boosted by up to one order of magnitude compared to isolated cooling clouds
independent of self-gravity. Self-gravity preserves the densest clouds way past
their $\sim 15\,\mathrm{Myr}$ cloud crushing time scales. This model could
provides a plausible in-situ origin for the observed molecular gas. Warm
ionised gas is also generated, almost independent of the cloud density. The
amount solely depend on the magnetic field configuration in the wind. For low
density clouds ($0.1\,\mathrm{cm}^{-3}$), the forming warm ionised gas can be
as much as 60 per cent of the initially atomic cloud mass. This could
contribute to observations of outflows with ionised gas sensitive tracers.
