Space-efficient RLZ-to-LZ77 conversion

Consider a text $T [1..n]$ prefixed by a reference sequence $R = T [1..\ell]$. We show how, given $R$ and the $z'$-phrase relative Lempel-Ziv parse of $T [\ell + 1..n]$ with respect to $R$, we can build the LZ77 parse of $T$ in $n\,\mathrm{polylog} (n)$ time and $O (\ell + z')$ total space.