  Mass estimates of black holes (BHs) in the centers of Active Galactic Nuclei
(AGN) often rely on the radius-luminosity relation. However, this relation,
usually probed by reverberation mapping (RM), is poorly constrained in the
high-luminosity and high-redshift ends due to the very long expected lag times.
Multiply imaged AGN may thus offer a unique opportunity to explore the
radius-luminosity relation at these ends. In addition to comprising several
magnified images which enable a more efficient light-curve sampling, the time
delay between multiple images of strongly lensed quasars can also aid in making
such RM measurements feasible on reasonable timescales: If the time delay is,
for example, of the order of the expected time lag, changes in the emission
lines in the leading image can be observed around the same time as the changes
in the continuum in the trailing image. In this work we probe the typical
time-delay distribution in galaxy-cluster lenses and estimate the number of
both high-mass ($\sim10^9-10^{10}$ M$_{\odot}$), and high-redshift
($z\gtrsim4-12$) quasars that are expected to be strongly lensed by clusters.
We find that less than one, very massive (and luminous, L$_{UV}>10^{46.5}$ erg
s$^{-1}$) multiply imaged quasar is expected across the sky down to 30 AB mag.
Nonetheless, up to several dozen thousand M$_{BH}\sim10^{6}$-$10^{8}$
M$_{\odot}$ broad-line AGN at $z>4$ should be multiply imaged by galaxy
clusters and detectable with JWST, hundreds with $\textit{Euclid}$ and several
thousands with the $\textit{Roman}$ Space Telescope, across the whole sky.
These could supply an important calibration for the BH mass scaling in the
early Universe.
