$1ML$ $FeSe/SrTiO_{3}$ material, with $1$-monolayer of $FeSe$ grown on the $SrTiO_{3}$ substrate - mainly on the $(0,0,1)$ plane, the Fermi surface in the $FeSe$ monolayer is *electron-like *and* *centered at four M-points in the Brillouin zone - see more in [@Rebec-FeSe-TiO2], [@Sadovskii1-2]. The absence of the (nested) hole-bands on the Fermi surface rules out all $SFI$ nesting theories of pairing. Even the pairing between an electron- and incipient hole-band [@Hirschfeld-incipient] is ineffective since: ($1$) in the $FeSe$ monolayer the top of the hole band lies below the Fermi level around $60-80$ $meV$; ($2$) because of ($1$) the SFI coupling constant is (much) smaller than in the nesting case. This brings into play the interface interaction effects. The existence of *sharp replica bands* in the $ARPES$ spectra at energies of the order of optical phonons with $\Omega
\sim90$ $meV$, implies inevitably that the dominant interaction in $1ML$ $FeSe/SrTiO_{3}$ (and also in $1ML$ $FeSe/TiO_{2}$ [@Rebec-FeSe-TiO2]) is due to $EPI$ with strong forward scattering peak [@Lee-Interfacial-supplement]-[@Johnston1-2]. The physical mechanism for $EPI-FSP$ is material dependent and the basic physical quantities such as the width of the $FSP$, phonon frequencies and bare $EPI$ coupling can vary significantly from material to material. For instance, in $HTSC$-cuprates 