The smooth Hom-stack of an orbifold

For a compact manifold M and a differentiable stack \cX presented by a Lie groupoid X, we show the Hom-stack Hom(M,\cX) is presented by a Fr'echet-Lie groupoid Map(M,X) and so is an infinite-dimensional differentiable stack. We further show that if \cX is an orbifold, presented by a proper 'etale Lie groupoid, then Map(M,X) is proper 'etale and so presents an infinite-dimensional orbifold.