Energy transfer from Zeeman to dipolar order discovered by Jeener et al. is usually observed in solids with a strong dipole-dipole interaction of nuclear spins. It is not observed in liquids, where fast molecular motion completely averages this interaction. The intermediate case, when the dipole-dipole interaction of nuclear spins is only partially averaged, has been poorly studied. We report on the first measurement of an angular-dependent proton spin relaxation of a dipolar reservoir in mobile water molecules confined in the interlayer pores of a vermiculite single crystal. In this layered crystal, the intramolecular dipole-dipole interactions of nuclear spins are only partially averaged due to the restricted anisotropic molecular motion in nanopores. We show that this allows the formation of dipolar echo. We measured the spin-lattice relaxation times of the dipolar order T1D at different angles between the normal to the crystal surface and the applied magnetic field and obtained a distinct angular dependence of T1D. The minimum relaxation rate R1D was found around the magic angle of 54.74°.