Let the riemann mapping theorem be
Let $D\subset \mathbb{C}$ be a simply-connected domain and $z_0 \in D$. Then there exists a unique conformal map $f$ from $D$ onto the open unitdisk $\mathbb{D} = \lbrace z \in \mathbb{C} \ | \ |z| < 1 \rbrace$ with $f(z_0) = 0$.
A text Im reading now uses this for mapping $\hat{\mathbb{C}} \setminus \overline{B}$ conformal onto $\hat{\mathbb{C}} \setminus \overline{\mathbb{D}}$ with $f(\infty) = \infty$ (where $\hat{\mathbb{C}} = \mathbb{C} \cup \lbrace \infty \rbrace$ and $B$ is a simply-connected domain that contains the point $0$). How can one show that this is always allowed by the riemann mapping theorem?