We demonstrate that a microwave signal carried by a packet of dipolar spin waves propagating in a tangentially magnetized magnetic film can be stored in the form of standing dipole-exchange spin-wave modes of the film and can be recovered by means of a double-frequency parametric pumping mechanism. This mechanism is based on the parametric amplification of the standing (thickness) modes of the film by external pumping. The time of recovery, duration, and power of the recovered pulse signal are controlled by the power of the pumping signal.