  Let $A$ and $B$ be arbitrary $C^*$-algebras, we prove that the existence of a
Hilbert $A$-$B$-bimodule of finite index ensures that the WEP, QWEP, and LLP
along with other finite-dimensional approximation properties such as CBAP and
(S)OAP are shared by $A$ and $B$. For this, we first study the stability of the
WEP, QWEP and LLP under Morita equivalence of $C^*$-algebras.
  We present examples of Hilbert $A$-$B$-bimodules which are not of finite
index, while such properties are shared between $A$ and $B$. To this end, we
study twisted crossed products by amenable discrete groups.
