  We showed that the all phonons -- not only forward-scattering phonon but also
local (all-momentum-scattering) phonon -- contribute to boosting $T_c$ of the
$s^{\pm}$-wave pairing state in the incipient band model. In particular, when
the incipient band sinks deeper, the phonon boost effect of the local phonon
increases and becomes as effective as the one of the forward-scattering phonon.
Our finding implies that all interface phonons -- not only the 90 $meV$
Fuchs-Kliewer (F-K) phonon but also the 60 $meV$ F-K phonon -- from the
SrTiO$_3$ substrate and all intrinsic phonons of the FeSe monolayer itself
should contribute to increase $T_c$ of the FeSe/STO monolayer system.
