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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 ${\widehat{\mathfrak{sl}_2}}_{,1}$, andthus for generic weights we find the decomposition of the tensor product intoirreducibles of ${\widehat{\mathfrak{sl}_2}}_{,k+1} \oplus \mathsf{Vir}$. Theconstruction uses Wakimoto representations of${\widehat{\mathfrak{sl}_2}}_{,k}$, but the obtained vectors can be mapped backto Verma modules. Singularities of this mapping are cancelled by arenormalization. A detailed study of ``degenerations'' of Wakimoto modulesallowed to find the renormalization factor explicitly. The obtained result is asignificant step forward in a proof of equivalence of certain two-dimesnionalCFT models.

Decomposition of ${\widehat{\mathfrak{sl}_2}}_{,k} \ \oplus \  {\widehat{\mathfrak{sl}_2}}_{,1}$ highest weight representations for generic  level $k$ and equivalence between two dimensional CFT models