  We solve the loop equations of the $\beta$-ensemble model analogously to the
solution found for the Hermitian matrices $\beta=1$. For \beta=1$, the solution
was expressed using the algebraic spectral curve of equation $y^2=U(x)$. For
arbitrary $\beta$, the spectral curve converts into a Schr\"odinger equation
$((\hbar\partial)^2-U(x))\psi(x)=0$ with $\hbar\propto
(\sqrt\beta-1/\sqrt\beta)/N$. This paper is similar to the sister paper~I, in
particular, all the main ingredients specific for the algebraic solution of the
problem remain the same, but here we present the second approach to finding a
solution of loop equations using sectorwise definition of resolvents. Being
technically more involved, it allows defining consistently the B-cycle
structure of the obtained quantum algebraic curve (a D-module of the form
$y^2-U(x)$, where $[y,x]=\hbar$) and to construct explicitly the correlation
functions and the corresponding symplectic invariants $F_h$, or the terms of
the free energy, in 1/N^2$-expansion at arbitrary $\hbar$. The set of "flat"
coordinates comprises the potential times $t_k$ and the occupation numbers
\widetilde{\epsilon}_\alpha$. We define and investigate the properties of the
A- and B-cycles, forms of 1st, 2nd and 3rd kind, and the Riemann bilinear
identities. We use these identities to find explicitly the singular part of
$\mathcal F_0$ that depends exclusively on $\widetilde{\epsilon}_\alpha$.
