A search for the $B^0_s !rightarrow D^{*pm} D^mp$ decay is performed using proton-proton collision data at centre-of-mass energies of $7$, $8$ and $13,text{TeV}$ collected by the LHCb experiment, corresponding to an integrated luminosity of $9,text{fb}^{-1}$. The decay is observed with a high significance and its branching fraction relative to the $B^0 !rightarrow D^{*pm} D^mp$ decay is measured to be begin{align*} frac{mathcal{B}(B_s^0 rightarrow D^{ast pm} D^{mp}) }{mathcal{B}(B^0 rightarrow D^{ast pm} D^{mp}) } = 0.137 pm 0.017 pm 0.002 pm 0.006 ,, end{align*} where the first uncertainty is statistical, the second systematic and the third is due to the uncertainty on the ratio of the $B_s^0$ and $B^0$ hadronisation fractions.