Let $k$ be an algebraic closed field. Let $T, T'$ be algebraic Tori in the classical sense, meaning $T \cong \mathbb{A}_k^n \setminus V(X_1 \cdots X_n)$, $T' \cong \mathbb{A}_k^{n'} \setminus V(X_1 \cdots X_{n'})$. Let $M$ and $M'$ denote the associated character groups.
Now, let $i: T \to T'$ be an inclusion of tori, meaning that it is a morphism of varieties and a group homomorphism and injective. It induces a group homomorphism $\hat{i}: M' \to M$ via $\chi^{m'} \mapsto \chi^{m'} \circ i$.
Question: Is it in general true that $\hat{i}$ is surjective?
This question arose while studying Proposition $1.1.8$ in "Toric Varieties" from Cox, Little and Schenck. In fact I don't have an idea why it should be true, but it seems to me that they use this fact.
Thanks for any help.