Is the impression of an ideal boundary point (=end) the union of the impressions of the prime ends of the circle of prime ends associated to this end?

Question

Let S be a compact orientable surface and U an open connected subset of S with finitely many ideal boundary points (or ends). U has a prime ends compactification which is a surface with boundary (following Mather). Let b be one of these ideal boundary points and Z(b) its impression in S. If Z(b) has more than one point, then there is a circle C(b) of prime ends associated to b. Each prime end e of C(b) has its impression Y(e) (another impression, the intersection of the closures of the sets of a chain that define e). This seem to be known by experts, but I could not find it written anywhere. Does anybody knows how to prove it? Knows a reference? I think I can prove it using scaffolds, a powerful tool created by Mather to prove various properties of prime ends. But it is a lot of work. Any good hint? Thanks.