  This article provides an account of the functorial correspondence between
irreducible singular $G$-monopoles on $S^1\times \Sigma$ and $\vec{t}$-stable
meromorphic pairs on $\Sigma$. The main theorem of [1] is thus generalized here
from unitary to arbitrary compact, connected gauge groups. The required
distinctions and similarities for unitary versus arbitrary gauge are clearly
outlined and many parallels are drawn for easy transition. Once the
correspondence theorem is complete, the spectral decomposition is addressed.
