Abstract: The first full angular analysis of the B0 -> D-Ds+ decay is performed using 6 fb(-1) of pp collision data collected with the LHCb experiment at a centre-of-mass energy of 13 TeV. The Ds+-> Ds+gamma and D*- -> D<overbar></mml:mover>0- vector meson decays are used with the subsequent Ds+ -> K+K-pi (+) and D<overbar></mml:mover>0 -> K+pi (-) decays. All helicity amplitudes and phases are measured, and the longitudinal polarisation fraction is determined to be f(L) = 0.578 +/- 0.010 +/- 0.011 with world-best precision, where the first uncertainty is statistical and the second is systematic. The pattern of helicity amplitude magnitudes is found to align with expectations from quark-helicity conservation in B decays. The ratio of branching fractions [B(B0 -> D-Ds+) x B(Ds+-> Ds+gamma)]/B(B-0 -> D(*-)Ds+) is measured to be 2.045 +/- 0.022 +/- 0.071 with world-best precision. In addition, the first observation of the Cabibbo-suppressed B-s -> D(*-)Ds+ decay is made with a significance of seven standard deviations. The branching fraction ratio B(B-s -> D(*-)Ds<mml:mo>+)/B(B-0 -> D(*-)Ds<mml:mo>+) is measured to be 0.049 +/- 0.006 +/- 0.003 +/- 0.002, where the third uncertainty is due to limited knowledge of the ratio of fragmentation fractions.<fig id=“Figa” position=“anchor”><graphic position=“anchor” specific-use=“HTML” mime-subtype=“JPEG” xmlns:xlink=“http://www.w3.org/1999/xlink” xlink:href=“MediaObjects/13130202116089FigaHTML.jpg” id=“MO1”></graphic