In solid-state NMR spectroscopy, the through-space transfer of magnetization from protons to quadrupolar nuclei is employed to probe proximities between those isotopes. Furthermore, such transfer, in conjunction with Dynamic Nuclear Polarization (DNP), can enhance the NMR sensitivity of quadrupolar nuclei, as it allows the transfer of DNP-enhanced 1H polarization to surrounding nuclei. We compare here the performances of two approaches to achieve such transfer: PRESTO (Phase-shifted Recoupling Effects a Smooth Transfer of Order), which is currently the method of choice to achieve the magnetization transfer from protons to quadrupolar nuclei and which has been shown to supersede Cross-Polarization under Magic-Angle Spinning (MAS) for quadrupolar nuclei and D-RINEPT (Dipolar-mediated Refocused Insensitive Nuclei Enhanced by Polarization Transfer) using symmetry-based 〖SR4〗_1^2 recoupling, which has already been employed to transfer the magnetization in the reverse way from half-integer quadrupolar spin to protons. We also test the PRESTO sequence with 〖R16〗_7^6 recoupling using 270090180 composite π-pulses as inversion elements. This recoupling scheme, which has previously been proposed to reintroduce 1H Chemical Shift Anisotropy (CSA) at high MAS frequencies with high robustness to rf-field inhomogeneity, has not so far been employed to reintroduce dipolar couplings with protons. These various techniques to transfer the magnetization from protons to quadrupolar nuclei are analyzed using (i) an average Hamiltonian theory, (ii) numerical simulations of spin dynamics, and (iii) experimental 1H  27Al and 1H  17O transfers in as-synthesized AlPO4-14 and 17O-labelled fumed silica, respectively. The experiments and simulations are done at two magnetic fields (9.4 and 18.8 T) and several spinning speeds (15, 18-24 and 60 kHz). This analysis indicates that owing to its -encoded character, PRESTO yields the highest transfer efficiency at low magnetic fields and MAS frequencies, whereas owing to its higher robustness to rf-field inhomogeneity and chemical shifts, D-RINEPT is more sensitive at high fields and MAS frequencies, notably for protons exhibiting large offset or CSA, such as those involved in hydrogen bonds.