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It is proved, using so-called multirectangular invariants, that the condition αβ = α̃β̃ is sufficient for the isomorphism of the spaces $E₀\left(exp\alpha i\right)\otimes ̂E_{\infty }\left(exp\beta j\right)$ and $E₀\left(exp\alpha ̃i\right)\otimes ̂E_{\infty }\left(exp\beta ̃j\right)$. This solves a problem posed in [14, 15, 1]. Notice that the necessity has been proved earlier in [14].