Let A,B,C,D be tame (not wild) n-1-spheres inside the n-sphere S such that $A\cap B = C \cap D = \emptyset$. Let also $f: A \rightarrow C$ and $g: B \rightarrow D$ be two homeomorphisms. Is there any homeomorphism $h: S \rightarrow S$ that extends f and g?
If it is false, in which dimensions is it true?