  In this paper, we introduce right-invariant (similarly, left-invariant)
Poisson-Nijenhuis Structures on Lie groupoids and their infinitesimal
counterparts as called $(\Lambda , \mathbf{n})-$structures. We present a mutual
correspondence between $(\Lambda ,\mathbf{n})-$structures on Lie algebroids
with Poisson-Nijenhuis structures $(\Pi , \mathbf{N})$ on their Lie groupoids
under some conditions. Also, we will construct Poisson-Nijenhuis pair groupoids
as an example from the invariance's point of view.
