  Using predictions in mirror symmetry, C\u{a}ld\u{a}raru, He, and Huang
recently formulated a "Moonshine Conjecture at Landau-Ginzburg points" for
Klein's modular $j$-function at $j=0$ and $j=1728.$ The conjecture asserts that
the $j$-function, when specialized at specific flat coordinates on the moduli
spaces of versal deformations of the corresponding CM elliptic curves, yields
simple rational functions. We prove this conjecture, and show that these
rational functions arise from classical $ _2F_1$-hypergeometric inversion
formulae for the $j$-function.
