  We report on our on-going study of the $B_s \to K\ell\nu$ decay in $N_f=2+1$
lattice QCD. We employ fully relativistic setup in which the M\"obius
domain-wall action is used for all quark flavors. The lattice cutoff is $a^{-1}
\sim 2.5$ GeV, where we take bottom quark masses up to $m_Q\!<\!0.7a^{-1}$ in
order to control discretization errors. We present preliminary results for the
relevant form factors extracted from correlator ratios by inspecting their
ground state saturation.
