l}}^{\dagger }B_{{\bf l}}+B_{{\bf l}%
}^{\dagger }C_{{\bf l}}+C_{{\bf l}}^{\dagger }D_{{\bf l}}+D_{{\bf l}%
}^{\dagger }A_{{\bf l}}+H.c.]  \nonumber \\
&&-t^{\prime }\sum_{{\bf n}}[A_{{\bf l-x}}^{\dagger }B_{{\bf l}}+B_{{\bf l+y}%
}^{\dagger }C_{{\bf l}}+C_{{\bf l+x}}^{\dagger }D_{{\bf l}}+D_{{\bf l-y}%
}^{\dagger }A_{{\bf l}}+H.c.],  \nonumber\end{aligned}$$ where ${\bf l}$ numbers octahedra rather than individual sites, ${\bf x}%
=(1,0)$, and ${\bf y}=(0,1)$. A Fourier transformation and diagonalization of a $4\times 4$ matrix yields the bipolaron spectrum: $$E_{2}({\bf K})=V_{c}-3.23E_{p}\pm 2t^{\prime }[\cos (K_{x}/2)\pm
\cos (K_{y}/2)].  \label{tseventeen}$$ There are four bipolaronic subbands combined in the band of the width $%
8t^{\prime }$. The effective mass of the lowest band is $m^{\ast
\ast }=2/t^{\prime }$. The bipolaron binding energy is $\Delta
\approx 1.23E_{p}-V_{c}.$ Inter-site bipolarons already move in the [*first*]{} order of the single polaron hopping. This remarkable property is entirely due to the strong on-site repulsion and long-range electron-phonon interactions that leads to a non-trivial connectivity of the lattice. This fact combines with a weak renormalization of $t^{\prime }$ yielding a [*superlight*]{} bipolaron with the mass $m^{\ast \ast }\propto \exp
(0.60\,E_{p}/\omega )$. We recall that in the Holstein model $m^{\ast \ast }\propto \exp (2E_{p}/\omega )$ [@aleran]. Thus the mass of the Fröhlich bipolaron in the perovskite layer scales approximately as a [*cubic root*]{} of that of 