How to construct Gorenstein projective modules relative to complete duality pairs over Morita rings

Let $\Delta =\left(\begin{smallmatrix} A & {_AN_B}\\ {_BM_A} B \\\end{smallmatrix}\right)$ be a Morita ring with $M\otimes_{A}N=0=N\otimes_{B}M$.We first study how to construct (complete) duality pairs of $\Delta$-modules using $A$-modules and $B$-modules, generalizing the result Mao (Comm. Algebra, 2020, 12: 5296--5310) about over triangular matrix ring. Moreover, we Gorenstein projective modules relative complete $\Delta$-modules. Finally, give an application Ding modules.