The concepts of an intrinsically projective module and an intrinsically injective module are introduced and their connection with the presence of annihilator conditions in the endomorphism ring of a module is explained. It is shown that a ring $R$ is quasi-Frobenius if and only if in the endomorphism ring of any fully projective (or any fully injective) $R$-module it is true that $r(l(I))=I$ and $l(r(J))=J$ for all finitely generated right ideals $I$ and finitely generated left ideals $J$.