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We present a simple analytical model for studying the collapse of an ultracompact stellar object (regular black hole mimicker with infinite redshift surface) to form a (integrable) black hole, in the framework of general relativity. Both initial and final configurations have the same ADM mass, so the transition represents an internal redistribution of matter without emission of energy. The model, despite being quite idealized, can be viewed as a good starting point to investigate near-horizon quantum physics.