In the proof that a simplicial group G is always Kan (see e.g. https://ncatlab.org/nlab/show/simplicial+group#AsKanComplexes ), you can always fill a $(m, j)$-horn $\lambda$ to a $m$-simplex $x$ with an algorithm. Let's call $x:=\mu^m_j(\lambda)$ the filler of $\lambda$.
Let $\lambda$ be the $(m, j)$-horn of a degenerate simplex $s_i(y)$ for some $i$, that is, $\lambda = p^m_j \circ s_i (y)$, where $p^m_j: G_m \to Hom(\Lambda^m_j, G)$ is the horn projection. Then is the filler $\mu^m_j( \lambda)=y$? Namely, is the (Moore) filler of the horn of a degenerate simplex itself? At least when $G$ is a simplicial abelian group?
We can verify this in some lower cases, but I doubt this might be classical in homotopy theory. However, I can't find any references. Thanks a lot!!