  We show the existence of "Zagier duality" between vector valued harmonic weak
Maass forms and vector valued weakly holomorphic modular forms of integral
weight. This duality phenomenon arises naturally in the context of harmonic
weak Maass forms as developed in recent works by Bruinier, Funke, Ono, and
Rhoades. Concerning the isomorphism between the spaces of scalar and vector
valued harmonic weak Maass forms of integral weight, "Zagier duality" between
scalar valued ones is derived.
