The Dold-Kan correspondence between the category of simplicial abelian groups and the category of non-negatively graded chain complexes of abelian groups is a classical result. It states that the normalization functor $N$, which sends a simplicial abelian group to a normalized chain complex, possesses an adjoint functor $D$ such that $$N : s(Ab) \to Ch_{\geq 0}(Ab): D$$ is an equivalence of categories.

Also, we know that there is another construction, called the Moore complex functor, $M :  s(Ab) \to Ch_{\geq 0}(Ab)$, given by $M(A_*)_n = A_n$ and the differentials are just alternating sums of face maps.

I think there should be an analogue of Dold-Kan correspondence in the category of Symmetric spectra in the sense of Hovey-Shipley-Smith.

Is there any possibility of a Quillen adjoint functor of $M?$