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