We have chosen the ${\overline{B}}^0\to D^{⁎+}{\overline{D}}^{⁎0}{K}^{-}$ reaction in order to observe the $I=0,J^P=1^{+}$ ($R_1$) partner state of the $X_0\left(2866\right)$ stemming from the $D^{⁎}{\overline{K}}^{⁎}$ molecular picture. The reaction proceeds via external emission in the most favored Cabibbo decay mode and one observes the $R_1$ state as a very strong peak versus the background in the $D^{⁎+}{K}^{-}$ spectrum. The branching ratio for $R_1$ production in this reaction is estimated of the order of $4\times {10}^{-3}$. The method used, applied to the $B^{+}\to D^{-}{D}^{+}{K}^{+}$ reaction, produces a ratio of signal to background in the $D^{-}{K}^{+}$ spectrum in very good agreement with the LHCb experiment that observed the $X_0\left(2866\right)$.