  In this paper, we first generalize the theorem about the existence of an
enveloping action to a partial twisted smash product. Second, we construct a
Morita context between the partial twisted smash product and the twisted smash
product related to the enveloping action. Furthermore, we show some results
relating partial actions and partial representations over the partial twisted
smash products, which generalize the results of Alves and Batista (Comm.
Algebra, 38(8): 2872-2902, 2010). Finally, we present versions of the duality
theorems of Blattner-Montgomery for partial twisted smash products.
