Evaporation-residue-gated high-energy gamma-ray spectra were measured in the ¹⁹F+²⁷Al reaction at two beam energies of ~75 and 125 MeV. The compound nuclear angular momenta populated at the higher energy should extend beyond the critical value for the Jacobi shape transition, while those at the lower energy should be mostly restricted below the critical value. A sharp low-energy (at ~10 MeV) component has been observed in the gamma-ray strength function superimposed on a broad distribution. At the higher beam energy, the component becomes more prominent at higher angular momentum, whereas an opposite behavior is witnessed at the lower beam energy. The implication of these observations in connection with the occurrence of the Jacobi shape transition is discussed.