= Solution
A <structure embedding> preserves and reflects all <atomic formulas>, hence all <quantifier-free formulas> by induction on Boolean combinations. If $T$ has <quantifier elimination>, replace any $\varphi(\mathbf x)$ by a quantifier-free $\theta(\mathbf x)$ equivalent over $T$. For $\mathcal A\subseteq\mathcal B\models T$ and a tuple $\mathbf a$ from $A$,
$$
\mathcal A\models\varphi(\mathbf a)\iff\mathcal A\models\theta(\mathbf a)\iff\mathcal B\models\theta(\mathbf a)\iff\mathcal B\models\varphi(\mathbf a).
$$
Thus $\mathcal A\preceq\mathcal B$, and the preceding criterion proves $\boxed{\text{quantifier elimination implies model completeness}.}$
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