Let $R$ be a ring. An $R$-module $M$ is called FL (FP) if it has a finite resolution consisiting of finitely generated free (projective) modules.

Given an exact sequence of $R$-modules, $0\to M_1\to M_2\to M_3\to 0$, if two of the modules $M_1$, $M_2$ or $M_3$ are  FP, then the third is FP as well. This follows, for example,  from Proposition 1.4 and Proposition 4.1b of 

Bieri, Robert Homological dimension of discrete groups. Second edition. Queen Mary College Mathematics Notes. Queen Mary College, Department of Pure Mathematics, London, 1981.

My question is 

    

> If two of the modules $M_1$, $M_2$ or $M_3$ are  FL, is it true that
> the third one is also FL?