I heard that if $[X_0/G_0]$ and $[X_1/G_1]$ are differentiable stacks, then any morphism between them is naturally equivalent to
$$(G_0 \rightrightarrows X_0) \xleftarrow{\simeq} (G_2 \rightrightarrows X_2) \xrightarrow{F} (G_1 \rightrightarrows X_1)$$
where the left arrow is morita morphism and the right one is a Lie groupoid morphism.
I can't find a proof of this. Where can I find a detailed proof of this proposition?