RO-NMO 2000 Problem 123

We say that the abelian group $G$ has property (P) if, for any commutative group $H,$ any $H'\le H$ and any momorphism $\mu':H\longrightarrow G,$ there exists a morphism $\mu :H\longrightarrow G$ such that $\mu\bigg|_{H'} =\mu' .$ Show that:

a) the group $\left( \mathbb{Q}^*,\cdot \right)$ hasn't property (P). b) the group $\left( \mathbb{Q}, +\right)$ has property (P).