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Femtosecond laser pulses can induce ultrafast demagnetization as well as generate bursts of hot-electron spin currents. In trilayer spin valves consisting of two metallic ferromagnetic layers separated by a nonmagnetic one, hot-electron spin currents excited by an ultrashort laser pulse propagate from the first ferromagnetic layer through the spacer, reaching the second magnetic layer. When the magnetizations of the two magnetic layers are noncollinear, this spin current exerts a torque on magnetic moments in the second ferromagnet. Since this torque is acting only within the subpicosecond timescale, it excites coherent high-frequency magnons, as recently demonstrated in experiments. Here, we calculate the temporal shape of the hot-electron spin currents using the superdiffusive transport model and simulate the response of the magnetic system to the resulting ultrashort spin-transfer torque pulse by means of atomistic spin-dynamics simulations. Our results confirm that the acting spin-current pulse is short enough to excite magnons with frequencies beyond 1 THz, a frequency range out of reach for current-induced spin-transfer torques. We demonstrate the formation of thickness-dependent standing spin waves during the first picoseconds after laser excitation. In addition, we vary the penetration depth of the spin-transfer torque to reveal its influence on the excited magnons. Our simulations clearly show a suppression effect of magnons with short wavelengths already for penetration depths in the range of 1 nm, confirming experimental findings reporting penetration depths below 2 nm.