  We report on the calculation of the inclusive semileptonic decay of the $D_s$
meson on the lattice. We simulate the $D_s \rightarrow X_s\ell\nu_\ell$ process
with M\"obius domain-wall charm and strange quarks, whose masses were
approximately tuned to the physical values. We cover the whole kinematical
region. The focus of this work is on the systematic error due to finite-volume
effects. We construct a model of two-body final states to describe the data on
a finite volume lattice of $L \simeq 0.055 \, \text{fm}$ to investigate the
extrapolation to the infinite-volume limit.
