Finite separable field extensions with prescribed extensions of valuations. II

Let A¹,...,A^k be pairwise independent valuation rings of K. Prescribing extensions Δ _i ^j . of the value group Γ^j and extensions (mathfrak{L}_i^j) of the residue field (H^j) of A^j (i=1,...,r^j) such that (sumlimits_{i = 1}^{r^j } {(Delta _i^j :Gamma ^j )} cdot [mathfrak{L}_i^j :H^j ] = n) , we provide sufficient conditions for the existence of a separable field extension L of K of degree n with exactly r^j pairwise independent valuation rings B _i ^j lying over A^j, which have Δ _i ^j as value groups and (mathfrak{L}_i^j) as residue fields.