# Jordan curve and Conformal maps

Let $$\mathbb D$$ be the unitary open disk, $$D$$ a bounded domain(open and connected) with boundary a jordan curve and $$f$$ a conformal map from $$\mathbb D$$ to $$D$$, is it true that we can extend $$f$$ as an homeomorphism from $$\overline{\mathbb D}$$ to $$\overline{D}$$? and if it is true, does it hold for two bounded domains with boundary a jordan curve?

And this implies a yes to the second question: If $$f_j:\overline{\Bbb D}\to \overline D_j$$ for $$j=1,2$$ are as above then $$f_2\circ f_1^{-1}:\overline D_1\to\overline D_2$$.