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We show that electric currents are induced in inversion asymmetric ferromagnets if the exchange splitting varies in time after excitation by laser pulses. We interpret this phenomenon as the magnetic variant of the inverse Edelstein effect. Based on ab initio calculations we determine the size of this effect in Co/Pt(111) and Mn/W(001) magnetic bilayer systems and investigate its dependence on the magnetization direction. The comparison of our theoretical results to experiments measuring the THz signal emitted after laser excitation suggests that ultrafast demagnetization in 3d transition metal ferromagnets is dominated by transverse spin fluctuations rather than by a reduction of the exchange splitting.