We prove that if $G$ is an Abelian $p$-group of length not exceeding $\omega$ and $H$ is its $p^{\omega +n}$-projective subgroup for $n\in \mathbb{N}\cup \left\{0\right\}$ such that $G/H$ is countable, then $G$ is also $p^{\omega +n}$-projective. This enlarges results of ours in (Arch. Math. (Brno), 2005, 2006 and 2007) as well as a classical result due to Wallace (J. Algebra, 1971).