Let $Q$ be a wild $n$-Kronecker quiver, i.e., a quiver with two vertices,
labeled by 1 and 2, and $n\geq 3$ arrows from 2 to 1. The indecomposable
regular modules with preprojective Gabriel-Roiter submodules, in particular,
those $\tau^{-i}X$ with $\udim X=(1,c)$ and $1\leq c\leq n-1$ will be studied.
It will be shown that for each $i\geq 1$ the irreducible monomorphisms starting
with $\tau^{-i}X$ are namely Gabriel-Roiter inclusions, and moreover, the
Gabriel-Roiter measures of these modules are `neighbors'.