We study the appearance of structures in the decay of the B− into K−π−D+s0(2317) and K−π−D+s1(2460) final states by forming invariant mass distributions of π−D+s0 and π−D+s1 pairs, respectively. The structure in the distribution is associated to the kinematical triangle singularity that appears when the B−→K−K∗0D0 ( B−→K−K∗0D∗0 ) decay process is followed by the decay of the K∗0 into π−K+ and the subsequent rescattering of the K+D0 ( K+D∗0 ) pair forming the D+s0(2317) ( D+s1(2460) resonance. We find this type of non-resonant peaks at 2850MeV in the invariant mass of π−Ds0 pairs from B−→K−π−D+s0(2317) decays and around 3000MeV in the invariant mass of π−D+s1 pairs from B−→K−π−D+s1(2460) decays. By employing the measured branching ratios of the B−→K−K∗0D0 and B−→K−K∗0D∗0 decays, we predict the branching ratios for the processes B− into K−π−D+s0(2317) and K−π−D+s1(2460) , in the vicinity of the triangle singularity peak, to be about 8×10−6 and 1×10−6 , respectively. The observation of this reaction would also give extra support to the molecular picture of the D+s0(2317) and D+s1(2460) .