$G$-projective groups

Let TF be the category of torsion free abelian groups of finite rank and homomorphisms. For $G$ in TF let ${\text{PC}}\left( G \right)$ be the projective class in TF generated by $\left\{ G \right\}$. Theorem. ${\text{PC}}\left( G \right)$ consists exactly of groups of the form $P \oplus F$, where $F$ is finite rank free and $P$ is $G$-projective $P \oplus P' \cong {G^n}$ for some positive integer $n$).