= Solution
Use positive jumps $\Delta T=T-T_\infty$ and $\Delta S=S-S_\infty$ for the hot salty lower reservoir. The <Boussinesq> density excess below the interface is proportional to $\beta\Delta S-\alpha\Delta T$. Static stability therefore requires
$$
\boxed{R_\rho=\frac{\beta\Delta S}{\alpha\Delta T}>1,}
$$
with one the neutral limiting value. For $R_\rho<1$ the lower layer is lighter overall and ordinary overturning <convection> replaces the statically stable interface.
In the stable hot-below, salty-below configuration, <thermal diffusivity> exceeds salt diffusivity. Heat transfer can destabilize thin adjacent fluid regions before the stabilizing salt difference is erased, causing the diffusive regime of <double-diffusive convection>. As $R_\rho\to\infty$, stabilization by salt dominates, interfacial convective exchange is strongly suppressed, and the specified heat-flux model tends to zero at fixed $\Delta T$. This limit is not a claim that molecular heat conduction itself ceases.
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