are the spectral weights. For the quasiparticle band $\omega_{1}$ one obtains $A_{1}=(1+\lambda_{m})^{-1}$, while for the replica bands at $\omega_{2}$ and $\omega_{3}$ one has $A_{2}=A_{3}=(\lambda_{m}/2)(1+\lambda_{m})^{-1}$. The ratio of the intensities at $T=0$ of the $\omega_{2}$ replica band and quasiparticle band $\omega_{1}$ is given by$$\frac{A_{2}(\mathbf{k}_{F},\omega,T=0)}{A_{1}(\mathbf{k}_{F},\omega
,T=0)}=\frac{\lambda_{m}}{2}. \label{ARPES-inten}$$ It is necessary to mention that at finite $T(>0)$ this ratio is changed as found in [@Johnston1-2]. In that case $\Sigma_{epi}^{(T)}(\mathbf{k\approx
k}_{F},\omega,T\neq0)\approx\lambda_{m}/(\omega+\Omega)$ which gives the quasiparticle and replica band $\omega_{1}^{(T)}=\Omega(-1+\sqrt
{1+4\lambda_{m}})/2$ and $\omega_{2}^{(T)}=-\Omega(1+\sqrt{1+4\lambda_{m}})/2$ and $(A_{2}/A_{1})_{T}=\lambda_{m}$ [@Steve-Kulic]. This intriguing difference of the $T=0$ and $T\neq0$ results for $(A_{2}/A_{1})$ in the $EPI-FSP$ theory, $(A_{2}/A_{1})_{T}=2(A_{2}/A_{1})_{0}$, is due to the sharpness of the Fermi function $n_{F}(\xi_{\mathbf{k+q}})$ entering in $\Sigma_{epi}(\mathbf{k},\omega)\ $- see $Eq.$(\[Sigma-integ\]) in Appendix [@Steve-Kulic].

We stress that, the $ARPES$ measurements of $A_{2}/A_{1}$ in $1ML$ $FeSe/SrTiO_{3}$ were done at finite temperatures ($T\neq0$) and in the $k=0$ point with $\xi(k=0)\sim-50$ $meV$ which gives $(A_{2}/A_{1})_{T}\approx0.15-0.2$ [@Lee-Interfacial-supplement], [@Replica-bands]. According to the theory in [@Lee-Interfacial-supplement], [@Johnston1-2] one obtains $\lambda_{m}^{(ARPES)}\approx0.15-0.2$. Below we show, that $\lambda_{m}$ can be also extracted from the formula $Eq.$(\[Tco\] ) for $T_{c0}\approx100$ $K$, which gives $\lambda
_{m}^{(T_{c0})}\approx0.18$. The latter value is in a good agreement with $\lambda_{m}^{(ARPES)}$ from $ARPES$ [@Steve-Kulic]. If we put this value in  $Eq.$(\[ARPES-inten\]) one obtains that 