We study an $R$-module $M$ in which every finitely generated submodule of $M$ is a kernel of an endomorphism of $M$. Such modules are called Co-epi-finite-retractable (CEFR). We also consider CEFR condition on the injective hull of simple modules, submodules and factors of a CEFR module and direct sum of CEFR modules. Among other results, we prove that the injective hull of a simple module over a commutative Noetherian ring, is uniserial if and only if it is CEFR. We investigate modules over a principal ideal ring, and show that all finitely generated torsion modules over a principal ideal domain are CEFR. Also, we show that every module over a commutative K\"othe ring is CEFR. We also observe that a ring $R$ is left pseudo morphic if and only if it is CEFR as a left $R$-module and we obtain some new properties of left pseudo morphic rings.
