The homomorphism of presheaves ${\mathrm{K}}_{\ast }^{\mathrm{M}\mathrm{W}}\to {\pi }_s^{\ast ,\ast }$ over a base

We construct the homomorphism of presheaves ${$\mathrm{K}$}^$\mathrm{M}\mathrm{W}$_* \to {\pi}^{,}$overanarbitrarybasescheme$S$,where$$\mathrm{K}$^$\mathrm{M}\mathrm{W}$$ is the (naive) Milnor-Witt K-theory presheave. Also we discuss some partly alternative proof (or proofs) of the isomorphism of sheaves ${\text{unKMW}}_n\simeq {\underset{‾}{\pi }}_s^{n,n}$, $n\in \mathbb{Z}$, over a filed $k$ originally proved in \cite{M02} and \cite{M-A1Top}.