If $(\alpha,\beta)$ is the factor pair congruences of algebra $\mathbb{A},$ ia $(\forall \gamma\in ConA)\alpha\circ\gamma=\gamma\circ\beta?$

Let $ \mathbb{A}$ be an algebra such that $ ConA$ is the distributive lattice. If $ (\alpha,\beta)$ is the factor pair congruences of algebra $ \mathbb{A},$ prove that $ (\forall \gamma\in ConA)\alpha\circ\gamma=\gamma\circ\beta.$