  The quantum Batalian-Vilkovisky master action for closed string field theory
consists of kinetic term and infinite number of interaction terms. The
interaction strengths (coupling constants) are given by integrating the
off-shell string measure over the distinct string diagrams describing the
elementary interactions of the closed strings. In the first paper of this
series, it was shown that the string diagrams describing the elementary
interactions can be characterized using the Riemann surfaces endowed with the
hyperbolic metric with constant curvature $-1$. In this paper, we construct the
off-shell bosonic-string measure as a function of the Fenchel-Nielsen
coordinates of the Teichm\"uller space of hyperbolic Riemann surfaces. We also
describe an explicit procedure for integrating the off-shell string measure
over the region inside the moduli space corresponding to the elementary
interactions of the closed strings.
