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Summary form only given. The most favorable conditions for positron-antiproton capture in traps can be provided when high-density clouds of accumulated antiprotons and positrons are brought and kept together by means of specially chosen electromagnetic field and strong cooling. However, the cross-section of the spontaneous recombination remains very small even at extremely low temperatures. The recombination rate may be increased in an external resonance field. In the present report the possibility of increase the recombination rate by means of laser pulses is estimated. An initial state of antiproton-positron system will belong to a continuous spectrum final state and to a discrete one. Taking into account the possibility to use short pulses, we analyzed system state after the laser pulse.