A $Q$-exact off-shell action is constructed for twisted abelian (2,0) theory on a Lorentzian six-manifold of the form $M_{1,5} = Ctimes M_4$, where $C$ is a flat two-manifold and $M_4$ is a general Euclidean four-manifold. The properties of this formulation, which is obtained by introducing two auxiliary fields, can be summarised by a commutative diagram where the Lagrangian and its stress-tensor arise from the $Q$-variation of two fermionic quantities $V$ and $lambda^{mu u}$. This completes and extends the analysis in [arXiv:1311.3300].
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