We give a constructive (algorithmic) proof that the quotient structure of finite k-labeled posets (forests) under 2-order is isomorphically embeddable into the corresponding structures under 0-order (also known as homomorphic order) and 1-order. In particular, it means that 2-preorder on the finite k-labeled posets (forests) can be split (in some specified sense) into 0-preorder and 2-equivalence. As a corollary, we define the infimum operation in the quotient structures of the finite k-labeled posets and forests, and prove that these structures are distributive lattices.
