  Let A#_{\alpha, \omega}H be a partial crossed product. In this paper, we
first generalize the theorem about the existence of an enveloping action to
twisted partial actions. Second, we construct a Morita context between the
partial crossed product and the crossed product related to the enveloping
action. Furthermore, we discuss equivalences of partial crossed products
Finally, we investigate when A\subset A#_{\alpha, \omega}H becomes a separable
extension.
