This is a continuation of our study of the foundations of D-branes from the viewpoint of Grothendieck in the region of the related Wilsons theory-space where branes are still branes. In this work, we focus on D-strings and construct the moduli stack
of morphisms from Azumaya prestable curves $C^{Az}$ with a fundamental module ${cal E}$ to a fixed target $Y$ of a given combinatorial type. Such a morphism gives a prototype for a Wick-rotated D-string of B-type on $Y$, following the Polchinski-Grothendieck Ansatz, and this stack serves as a ground toward a mathematical theory of topological D-string world-sheet instantons.
