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The baryon/skyrmion correspondence implies that the baryon number is encoded into a topological surface integral. Under certain conditions that we clarify, this surface integral can be measured by an asymptotic observer in form of an Aharonov-Bohm phase-shift in an experiment in which the skyrmion passes through a loop of a probe string. In such a setup the baryon/skyrmion number must be respected by black holes, despite the fact that it produces no long-range classical field. If initially swallowed by a black hole, the baryon number must resurface in form of a classical skyrmion hair, after the black hole evaporates below a certain critical size. Needless to say, the respect of the baryon number by black holes is expected to have potentially-interesting astrophysical consequences.