This paper presents a notebook-backed minimal W-boson branch-conversion bridge within the Emergent Condensate Superfluid Medium (ECSM) weak-sector programme. Previous ECSM work constructed a closure-active weak pair, recovered a minimal SU(2)L-like algebra, derived an ECSM electric-charge bridge through Q_ECSM = T3 + Y/2, and then showed that branch-phase and neutral closure-imbalance modes can coherently rotate into photon-like and Z-like neutral modes. The present work tests the missing charged weak-sector step: whether W+- and W--like modes can be represented as finite-response branch-conversion excitations between a neutral closure branch Q0 and a charged branch Qch. Using the inherited charge assignments Q(Q0) = 0, Q(Qch) = -1, the notebook verifies T+ |Qch> = |Q0>, T- |Q0> = |Qch>, with null actions T+ |Q0> = 0, T- |Qch> = 0. The corresponding charge transfers are W+ : -1 -> 0, Delta Q = +1, W- : 0 -> -1, Delta Q = -1. The notebook also tests the coherent-limit weak mass relation m_W^2 = m_0^2 g^2, together with the previous neutral result m_Z^2 = m_0^2(g^2 + g'^2), and verifies m_W / m_Z = cos(theta), with a coupling-ratio scan giving a maximum residual error of 2.22e-16, consistent with floating-point precision. A finite-response deformation test shows that the W/Z-like relation can drift away from coherence at chi < 1 but is recovered exactly as chi -> 1. Final notebook verdict: PASS_MINIMAL_W_BRANCH_CONVERSION_BRIDGE This paper does not claim to derive the full electroweak theory, physical W/Z masses, measured Weinberg angle, weak decay rates, scattering amplitudes, Higgs phenomenology, coupling running, CKM/PMNS mixing, or precision electroweak observables. Its narrower result is that ECSM can represent charged W+- and W--like weak modes as finite-response branch-conversion excitations carrying Delta Q = +/-1, with the expected coherent-limit mass relation m_W/m_Z = cos(theta).