  A theorem of Muhly-Renault-Williams states that if two locally compact
groupoids with Haar system are Morita equivalent, then their associated
convolution C*-algebras are strongly Morita equivalent.
  We give a new proof of this theorem for Lie groupoids. Subsequently, we prove
a counterpart of this theorem in Poisson geometry: If two Morita equivalent Lie
groupoids are s-connected and s-simply connected, then their associated Poisson
manifolds (viz. the dual bundles to their Lie algebroids) are Morita equivalent
in the sense of P. Xu.
