  We construct highest weight vectors of ${\widehat{\mathfrak{sl}_2}}_{,k+1}
\oplus \mathsf{Vir}$ in tensor products of highest weight modules of
${\widehat{\mathfrak{sl}_2}}_{,k}$ and ${\widehat{\mathfrak{sl}_2}}_{,1}$, and
thus for generic weights we find the decomposition of the tensor product into
irreducibles of ${\widehat{\mathfrak{sl}_2}}_{,k+1} \oplus \mathsf{Vir}$. The
construction uses Wakimoto representations of
${\widehat{\mathfrak{sl}_2}}_{,k}$, but the obtained vectors can be mapped back
to Verma modules. Singularities of this mapping are cancelled by a
renormalization. A detailed study of ``degenerations'' of Wakimoto modules
allowed to find the renormalization factor explicitly. The obtained result is a
significant step forward in a proof of equivalence of certain two-dimesnional
CFT models.
