  Let $E$ be a primarily quasilocal field, $M/E$ a finite Galois extension and
$D$ a central division $E$-algebra of index divisible by $[M\colon E]$. In
addition to the main result of Part I, this part of the paper shows that if the
Galois 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 the
character 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 the
multiplicative group $E ^{\ast}$ equals the intersection of the norm groups of
finite Galois extensions of $E$.
