= Solution
Distinguish the original <thiirane> <sulfur> $S_o$ from the <sulfur> $S_n$ supplied by <thiocyanate>. <sulfur> attack by $\mathrm{{}^-S_n{-}C\equiv N}$ at one <thiirane> <carbon> opens its C–$S_o$ bond with inversion. This produces a <thiolate> at the neighbouring <carbon> and a C–$S_n$–CN group at the attacked <carbon>. The OH-bearing remote <carbon> is unaffected.
The original <thiolate> $S_o^-$ now attacks the nitrile <carbon> intramolecularly. Shift one C≡N pi pair onto <nitrogen>. The resulting cyclic imidodithiocarbonate has the five-membered sequence \b[ring <carbon>–$S_o$–C(=N$^-$)–$S_n$–adjacent ring <carbon>]; its two <carbon> atoms are also part of the original six-membered carbocycle, exactly giving the hinted bicyclic intermediate.
Collapse can reform C≡N while breaking the nitrile-<carbon>–$S_n$ bond. This transfers the CN group to $S_o$ and generates $S_n^-$ as the <thiolate> on the other ring <carbon>. That <thiolate> attacks the remaining C–$S_o$ bond from the back, expelling $\mathrm{{}^-S_o{-}C\equiv N}$ and reclosing the <thiirane>. \b[Each <thiirane> <carbon> has undergone one inversion, so the new <sulfur> bridge lies on the opposite face; the OH configuration is retained.] The <thiocyanate> <sulfur> has entered the ring and the original ring <sulfur> has left as <thiocyanate>. This atom-labelled exchange mechanism explains how the same elemental formula can conceal <sulfur> replacement; <isotope> labelling would be needed to test that exchange experimentally. A single <epimerization> at the OH <carbon> would give the wrong <stereochemical> outcome.
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