How to implement the generalized-coherent-state POVM via nonadaptive continuous isotropic measurement

In a recent Letter~[PRL $\mathbf{\text{121}}$, 130404 (2018)], it was announced that the spin-coherent-state POVM can be implemented via a nonadaptive continuous isotropic measurement. In this article, the mathematical concepts used to prove this are explained in greater depth. Also provided is the more general result of how to implement a generalized-coherent-state POVM for any finite-dimensional unitary representation of a Lie group.