The interpretation of cosmic antiproton flux mea- surements from space-borne experiments is currently limited by the knowledge of the antiproton production cross-section in collisions between primary cosmic rays and the interstel- lar medium. Using collisions of protons with an energy of 6.5 TeV incident on helium nuclei at rest in the proximity of the interaction region of the LHCb experiment, the ratio of antiprotons originating from antihyperon decays to prompt production is measured for antiproton momenta between 12 and 110 GeV/c. The dominant antihyperon contribution, namely Λ → pπ + decays from promptly produced Λ par- ticles, is also exclusively measured. The results complement the measurement of prompt antiproton production obtained from the same data sample. At the energy scale of this mea- surement, the antihyperon contributions to antiproton pro- duction are observed to be significantly larger than predic- tions of commonly used hadronic production models.