This paper deals with a relation between homomorphisms of Moufang planes and homomorphisms of the corresponding Jordan algebras. The author proves in Theorem 1 and its Corollary that every Jordan homomorphism \(\sigma\) such that \((1[ij])^{\sigma}=1[ij]'\) implies a projective plane homomorphism. Theorems 2 and 3 are certain analogues of the fundamental theorem of projective geometry. The author has investigated a projective plane homomorphism while in the fundamental theorem one has a projective isomorphism. In Theorem 2 the author starts from a projective plane homomorphism \(\theta\), constructs a mapping \(\sigma\) of subsets of Jordan algebras and derives the properties of \(\sigma\). Theorem 2 shows that the suppositions of Theorem 1 are too strong. Therefore Theorem 3 presents a theorem with weaker condition as a converse of Theorem 2.