The paper presents the results of calculating the absorption spectrum of a phosphorus monoxide (PO) molecule corresponding to the A2Σ+(v'=0)-X2Π(v''=0) transition. The efficiency of excitation of the PO molecule is estimated as a function of the spectral parameters of the laser radiation. The positions of the fluorescence bands of PO are calculated. It is shown that the use of excitation wavelengths near the bandheads of the (P22+Q12) and P12 branches of the A2Σ+(v'=0)-X2Π3/2(v''=0) band provides spectral separation of the (0, 1) γ-band of the LIF of PO and vibrational-rotational Raman spectrum of atmospheric oxygen. The spectral responses of dimethyl methylphosphonate vapor in air under the action of KrF-laser radiation at a wavelength of 247.78 nm have been experimentally studied. In the wavelength range 252-260 nm, the (0, 1) γ-band of the LIF of PO-fragments and the vibrational-rotational band of spontaneous Raman scattering on oxygen molecules are unambiguously interpreted. It is shown that the results of calculations of the shape and position of the fluorescence spectra are in good agreement with the experimental data.