Аннотация:This paper reports the observation of the decays B(s)0B(s)0 → Ds1s1(2536)∓∓K±± using proton-proton collision data collected by the LHCb experiment, corresponding to an integrated luminosity of 9 fb−1−1. The branching fractions of these decays are measured relative to the normalisation channel B00→D‾0D0K++K−−. The Ds1s1(2536)−− meson is reconstructed in the D‾∗D∗(2007)00K−− decay channel and the products of branching fractions are measured to beB(Bs0→Ds1(2536)∓K±)×B(Ds1(2536)−→D‾∗(2007)0K−)=(2.49±0.11±0.12±0.25±0.06)×10−5,B(B0→Ds1(2536)∓K±)×B(Ds1(2536)−→D‾∗(2007)0K−)=(0.510±0.021±0.036±0.050)×10−5.B(Bs0→Ds1(2536)∓K±)×B(Ds1(2536)−→D∗(2007)0K−)=(2.49±0.11±0.12±0.25±0.06)×10−5,B(B0→Ds1(2536)∓K±)×B(Ds1(2536)−→D∗(2007)0K−)=(0.510±0.021±0.036±0.050)×10−5.The first uncertainty is statistical, the second systematic, and the third arises from the uncertainty of the branching fraction of the B00→D‾0D0K++K−− normalisation channel. The last uncertainty in the Bs0Bs0 result is due to the limited knowledge of the fragmentation fraction ratio, fss/fdd. The significance for the Bs0Bs0 and B00 signals is larger than 10 σ. The ratio of the helicity amplitudes which governs the angular distribution of the Ds1s1(2536)−−→D‾∗D∗(2007)00K−− decay is determined from the data. The ratio of the S- and D-wave amplitudes is found to be 1.11 ± 0.15 ± 0.06 and the phase difference between them 0.70 ± 0.09 ± 0.04 rad, where the first uncertainty is statistical and the second systematic.