Density of quasi-infinitely divisible random measures

Let $S$ be the underlying space, let $\mathcal{M}^{-}_{S}$ denote the space of signed measures on $S$, and let $\hat{\mathcal{M}}^{-}_{S}$ denote the space of bounded signed measures. Equip these spaces with their vague topologies, and equip $\hat{\mathcal{M}}^{-}_{S}$ additionally with its weak topology. A random measure is quasi-infinitely divisible (QID) if its distribution is quasi-infinitely divisible.

Density conjecture. Real-valued QID random measures are dense in the space of independently scattered real-valued random measures, regarded as random elements of $\mathcal{M}^{-}_{S}$ with the vague topology, under convergence in distribution. Likewise, bounded real-valued QID random measures are dense in the space of bounded independently scattered real-valued random measures, regarded as random elements of $\hat{\mathcal{M}}^{-}_{S}$ with either the vague topology or the weak topology, under convergence in distribution.

This conjecture proposes that quasi-infinitely divisible random measures approximate all independently scattered random measures in the indicated distributional topologies. The supplied text does not state whether the conjecture has been proved or disproved.