Laser-induced ultrafast demagnetization is an important phenomenon that probes arguably the ultimate limits of the angular momentum dynamics in solid. Unfortunately, many aspects of the dynamics remain unclear except that the demagnetization transfers the angular momentum eventually to the lattice. In particular, the role and origin of electron-carried spin currents in the demagnetization process are debated. Here we experimentally probe the spin current in the opposite phenomenon, i.e., laser-induced ultrafast magnetization of FeRh, where the laser pump pulse initiates the angular momentum build-up rather than its dissipation. Using the time-resolved magneto-optical Kerr effect, we directly measure the ultrafast-magnetization-driven spin current in a FeRh/Cu heterostructure. A strong correlation between the spin current and the magnetization dynamics of FeRh is found even though the spin filter effect is negligible in this opposite process. This result implies that the angular momentum build-up is achieved by an angular momentum transfer from the electron bath (supplier) to the magnon bath (receiver) and followed by the spatial transport of angular momentum (spin current) and dissipation of angular momentum to the phonon bath (spin relaxation).