The Two-Square Lemma and the connecting morphism in a preabelian category

We obtain a generalization of the Two-Square Lemma proved for abelian categories by Fay, Hardie, and Hilton in 1989 and (in a special case) for preabelian categories by Generalov in 1994. We also prove the equivalence up to sign of two definitions of a connecting morphism of the Snake Lemma.