  This is a continuation of the joint paper with the same title by A.Belenkiy
and Yu.Burago. It is proved here that two homeomorphic closed Alexandrov
surfaces (of bounded integral curvature) are bi-Lipschitz with a constant
depending only on upper bounds of their Euler number, diameters, negative
integral curvatures, and two positive numbers e and l such that positive
curvature of each embedded disk with perimeter not greater than l is not
greater than \pi-e.
