Morita equivalence for partially ordered monoids and po-$\Gamma$-semigroups with unities

We prove that operator pomonoids of a po-$\Gamma$-semigroup with unities are Morita equivalent pomonoids. Conversely, we show that if $L$ and $R$ are Morita equivalent pomonoids then a po-$\Gamma$-semigroup $A$ with unities can be constructed such that left and right operator pomonoids of $A$ are $Pos$-isomorphic to $L$ and $R$ respectively. Using this nice connection between po-$\Gamma$-semigroups and Morita equivalence for pomonoids we, in one hand, obtain some Morita invariants of pomonoids using the results of po-$\Gamma$-semigroups and on the other hand, some recent results of Morita theory of pomonoids are used to obtain some results of po-$\Gamma$-semigroups.