The main purpose of this work is to provide a framework for proving that, given a family of random maps known to converge in the Gromov--Hausdorff sense, then some (suitable) conditional families of random maps converge to the same limit. As a proof of concept, we show that quadrangulations with a simple boundary converge to the Brownian disk. More precisely, we fix a sequence of even positive integers with for some. Then, for the Gromov--Hausdorff topology, a quadrangulation with a simple boundary uniformly sampled among those with inner faces and boundary length weakly converges, in the usual scaling , toward the Brownian disk of perimeter.