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Let $C$ be a curve on a K3 surface $X$ with Picard group $\mathbb{Z}.[C]$.Mukai's program seeks to recover $X$ from $C$ by exhibiting it as aFourier-Mukai partner to a Brill-Noether locus of vector bundles on $C$. We usewall-crossing in the space of Bridgeland stability conditions to prove this forgenus $\ge14$. This paper deals with the case $g-1$ prime left over from PaperI.

Mukai's Program (reconstructing a K3 surface from a curve) via wall-crossing, II