  In this work we deal with partial (co)action of multiplier Hopf algebras on
not necessarily unital algebras. Our main goal is to construct a Morita context
relating the coinvariant algebra $R^{\underline{coA}}$ with a certain
subalgebra of the smash product $R\#\widehat{A}$. Besides this we present the
notion of partial Galois coaction, which is closely related to this Morita
context.
