$L'$-localization in an $\infty$-topos

We prove that, given any reflective subfibration $L_\bullet$ on an $\infty$-topos $\mathcal{E}$, there exists a reflective subfibration $L'_\bullet$ on $\mathcal{E}$ whose local maps are the $L$-separated maps, that is, the maps whose diagonals are $L$-local. This is the companion paper to "Localization theory in an $\infty$-topos".