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The paper is a continuation of the research on a one-to-one correspondencebetween $n$-dimensional spectral resolutions and $n$-dimensional observables onlexicographic types of quantum structures which started in \cite{DvLa4}. InPart I, we presented the main properties of $n$-dimensional spectralresolutions and observables, and we deeply studied characteristic points whichare crucial for our study. In present Part II, there is a main body of ourresearch. We investigate a one-to-one correspondence between $n$-dimensionalobservables and $n$-dimensional spectral resolutions with values in a kind of alexicographic form of quantum structures like perfect MV-algebras or perfecteffect algebras. The multidimensional version of this problem is morecomplicated than a one-dimensional one because if our algebraic structure is$k$-perfect for $k>1$, then even for the two-dimensional case of spectralresolutions we have more characteristic points. The obtained results areapplied to existence of an $n$-dimensional meet joint observable of $n$one-dimensional observables on a perfect MV-algebra and a sum of$n$-dimensional observables.

$n$-dimensional Observables on $k$-Perfect MV-Algebras and $k$-Perfect Effect Algebras. II. One-to-one Correspondence