  This is a sequel to the authors' article [BKO](arXiv:1901.02239). We consider
a hyperbolic knot $K$ in a closed 3-manifold $M$ and the cotangent bundle of
its complement $M \setminus K$. We equip $M \setminus K$ with a hyperbolic
metric $h$ and its cotangent bundle $T^*(M \setminus K)$ with the induced
kinetic energy Hamiltonian $H_h = \frac{1}{2} |p|_h^2$ and Sasakian almost
complex structure $J_h$, and associate a wrapped Fukaya category to
$T^*(M\setminus K)$ whose wrapping is given by $H_h$. We then consider the
conormal $\nu^*T$ of a horo-torus $T$ as its object. We prove that all
non-constant Hamiltonian chords are transversal and of Morse index 0 relative
to the horo-torus $T$, and so that the structure maps satisfy
$\widetilde{\mathfrak m}^k = 0$ unless $k \neq 2$ and an $A_\infty$-algebra
associated to $\nu^*T$ is reduced to a noncommutative algebra concentrated to
degree 0. We prove that the wrapped Floer cohomology $HW(\nu^*T; H_h)$ with
respect to $H_h$ is well-defined and isomorphic to the Knot Floer cohomology
$HW(\partial_\infty(M \setminus K))$ that was introduced in [BKO] for arbitrary
knot $K \subset M$. We also define a reduced cohomology, denoted by
$\widetilde{HW}^d(\partial_\infty(M \setminus K))$, by modding out constant
chords and prove that if $\widetilde{HW}^d(\partial_\infty(M \setminus K))\neq
0$ for some $d \geq 1$, then $K$ cannot be hyperbolic. On the other hand, we
prove that all torus knots have $\widetilde{HW}^1(\partial_\infty(M \setminus
K)) \neq 0$.
