  The BPS correlators of the symmetric product orbifold
$\text{Sym}_N(\mathbb{T}^4)$ are reproduced from the dual worldsheet theory
describing strings on $\text{AdS}_3\times {\rm S}^3\times \mathbb{T}^4$ with
minimal ($k=1$) NS-NS flux. More specifically, we show that the worldsheet
duals of the symmetric orbifold BPS states can be identified with their lift to
the covering surface, thereby making the matching of the correlators
essentially manifest. We also argue that the argument can be generalised to
arbitrary descendants, using suitable DDF operators on the worldsheet.
