  This is a continuation of our study of the foundations of D-branes from the
viewpoint of Grothendieck in the region of the related Wilson's 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.
