It has been commonly accepted that electromagnetic fields suppress superconductivity by inducing the ordered motion of Cooper pairs. We demonstrate a mechanism which instead provides generation of superconducting correlations by moving the superconducting condensate. This effect arises in superconductor/ferromagnet heterostructures in the presence of Rashba spin-orbit coupling or extrinsic impurity-induced spin-orbit coupling. We predict the odd-frequency spin-triplet superconducting correlations called the Berezinskii order to be switched on in ferromagnets at large distances from the superconductor/ferromagnet interface by application of a static magnetic field or irradiation inducing condensate motion in the direction perpendicular to structural anisotropy axis, what opens great perspectives for low-dissipative spintronics [1,2]. The effect is shown to result in the unusual behaviour of Josephson current under the applied magnetic field, supercurrent-controllable 0-π transitions and photo-induced Josephson current.