  We continue the work started in part I (q-alg/9706004) and prove the
invariance and universality in the class of finite type invariants of the
object defined and motivated there, namely the Aarhus integral of rational
homology 3-spheres. Our main tool in proving invariance is a translation scheme
that translates statements in multi-variable calculus (Gaussian integration,
integration by parts, etc.) to statements about diagrams. Using this scheme the
straight-forward "philosophical" calculus-level proofs of part I become
straight-forward honest diagram-level proofs here. The universality proof is
standard and utilizes a simple "locality" property of the Kontsevich integral.
