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The principal aim of this paper is to derive an abstract form of the thirdGreen identity associated with a proper extension $T$ of a symmetric operator$S$ in a Hilbert space $\mathfrak H$, employing the technique of quasi boundarytriples for $T$. The general results are illustrated with couplings ofSchr\"{o}dinger operators on Lipschitz domains on smooth, boundarylessRiemannian manifolds.

Coupling of symmetric operators and the third Green identity