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Let $E$ be a primarily quasilocal field, $M/E$ a finite Galois extension and$D$ a central division $E$-algebra of index divisible by $[M\colon E]$. Inaddition to the main result of Part I, this part of the paper shows that if theGalois group $G(M/E)$ is not nilpotent, then $M$ does not necessarily embed in$D$ as an $E$-subalgebra. When $E$ is quasilocal, we find the structure of thecharacter group of its absolute Galois group; this enables us to prove that if$E$ is strictly quasilocal and almost perfect, then the divisible part of themultiplicative group $E ^{\ast}$ equals the intersection of the norm groups offinite Galois extensions of $E$.

On the residue fields of Henselian valued stable fields, II