Mismatched Hartmann-Hahn conditions between the protons and dilute spins (such as N-15) are found to cause intermolecular magnetization transfer between the low-gamma nuclei over long distances. This transfer is purely proton mediated and occurs even in the absence of direct N-15-N-15 couplings. This has been demonstrated experimentally using a static single crystal of n-acetyl Leucine with intermolecular distances between the N-15 nuclei exceeding 6.5 angstrom. A quantum-mechanical explanation of this phenomenon is given based on the average Hamiltonian theory which was confirmed by detailed numerical many-spin simulations. The theory and experiment presented in the present paper may help in the development of solid-state NMR methods for studying interhelical contacts in membrane proteins, as well as for their spectral assignment.