= Solution
A <numéraire strategy> $\eta$ has zero consumption and strictly positive wealth
$$
N_t=X_t^{\nu,\eta}=\eta_{t+1}\cdot P_t>0
$$
at every date. Given an investment-consumption arbitrage $H$, retain its holdings and invest each nonnegative consumption $C_s^{0,H}$ in the numéraire. With
$$
A_t=\sum_{s=0}^t\frac{C_s^{0,H}}{N_s},
\qquad
K_t=H_t+A_{t-1}\eta_t,
$$
the self-financing identity for $\eta$ gives zero intermediate consumption for $K$. At a deterministic $T$ after a date at which positive consumption occurs with positive probability, liquidating gives
$$
C_T^{0,K}=C_T^{0,H}
+N_T\sum_{s=0}^{T-1}\frac{C_s^{0,H}}{N_s}\geq0.
$$
It is strictly positive with positive probability. Hence $K$ is a terminal-consumption arbitrage.
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