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Quantum coherence is an essential resource to gain advantage over classical physics and technology. Recently, it has been proposed that a low-temperature environment can induce quantum coherence of a spin without an external coherent pump. We address a critical question if such coherence is extractable by a weak coupling to an output system dynamically affecting back the spin-environment coupling. Describing the entire mechanism, we prove that such extraction is generically possible for output spins (also oscillators or fields) and, as well, in a fermionic analogue of such a process. We compare the internal spin coherence and output coherence over temperature and characteristic frequencies. The proposed optimal coherence extraction opens paths for the upcoming experimental tests with atomic and solid-state systems.