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Let $L$ be a finite lattice and let $I$ be an ideal of $L$. Then therestriction map is a bounded lattice homomorphism of the congruence latticeof~$L$ into the congruence lattice of $I$. In a 2009 paper, the authors provedthe converse.  In a 2012 paper, G. Cz\'edli proved an analogous result for rectangularlattices. In this paper, we prove a stronger form of Cz\'edli's result andprovide a short, elementary, and direct proof.

Homomorphisms of distributive lattices as restrictions of congruences. III. Rectangular lattices and two convex sublattices