The interplay of superconductivity and magnetism was studied in a composite prepared from ferromagnetic half-metallic La${}_{0.67}$Sr${}_{0.33}$MnO${}_{3}$ (LSMO) nanoparticles and the $s$-wave superconductor MgB${}_{2}$. A few principal effects have been found. With the onset of MgB${}_{2}$ superconductivity, a spectacular drop of the sample resistance was detected and complete superconductivity was observed at temperatures up to 20 K. The basic nanocomposite characteristics (critical temperature, current-voltage dependence, percolation threshold, etc.) are strongly affected by the half-metallic LSMO and, most probably, cannot be quantitatively explained within the framework of a conventional percolation scenario. Point contact (PC) spectroscopy was used to measure directly the superconducting energy coupling. For small voltage, an excess current and doubling of the PC normal-state conductance were detected. Conductance peaks corresponding to three energy gaps are clearly observed. Two of these gaps we identified as enhanced ${\ensuremath{\Delta}}_{\ensuremath{\pi}}$ and ${\ensuremath{\Delta}}_{\ensuremath{\sigma}}$ gaps originating from the MgB${}_{2}$; the third gap ${\ensuremath{\Delta}}_{\mathrm{tr}}$ is more than three times larger than the largest MgB${}_{2}$ gap. The temperature behavior of ${\ensuremath{\Delta}}_{\mathrm{tr}}$ does not follow the BCS dependence. The experimental results have a natural and qualitative explanation within the phase-coherency scenario of proximity-induced superconductivity. Specifically, at low temperature, a $p$-wave spin-triplet condensate with pairing energy ${\ensuremath{\Delta}}_{\mathrm{tr}}$ is essentially sustained in LSMO but is incapable of displaying a long-range superconducting response because of a phase-disordered state. The proximity coupling to MgB${}_{2}$ restores the long-range phase coherency of the superconducting state, which, in turn, enhances the superconducting state of the MgB${}_{2}$.