  Starting from the molecular picture for the $D_{s1}(2460)$ and $D_{s1}(2536)$
resonances, which are dynamically generated by the interaction of coupled
channels, the most important of which are the $D^*K$ for the $D_{s1}(2460)$ and
$DK^*$ for the $D_{s1}(2536)$, we evaluate the ratio of decay widths for the
$\bar{B}_s^0 \to D_{s1}(2460)^+ K^-$ and $\bar{B}_s^0 \to D_{s1}(2536)^+ K^-$
decays, the latter of which has been recently investigated by the LHCb
collaboration, and we obtain a ratio of the order of unity. The present results
should provide an incentive for the related decay into the $D_{s1}(2460)$
resonance to be performed, which would provide valuable information on the
nature of these two resonances.
