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It was recently argued that string theory on {\rm AdS}_3\times {\rm S}^3\times \mathbb{T}^4 with one unit (k=1) of NS-NS flux is exactly dual to the symmetric orbifold CFT {\rm Sym}^N(\mathbb{T}^4). In this paper we show how to directly relate the n-point correlators of the two sides to one another. In particular, we argue that the correlators of the world-sheet theory are delta-function-localised in string moduli space to those configurations that allow for a holomorphic covering map of the S^2-boundary of AdS_3 by the world-sheet. This striking feature can be seen both from a careful Ward identity analysis, as well as from semi-classically exact AdS3 solutions that are pinned to the boundary. The world-sheet correlators therefore have exactly the same structure as in the Lunin-Mathur construction of symmetric orbifold CFT correlators in terms of a covering surface --- which now gets identified with the world-sheet. Together with the results of 1803.04423 and 1812.01007 this essentially demonstrates how the k=1 AdS_3 string theory becomes equivalent to the spacetime orbifold CFT in the genus expansion.