= Solution
An $L$-embedding $\pi:A\to B$ is an <injective> map preserving the interpretations of all constants and functions and preserving and reflecting every relation. Explicitly $\pi(c^A)=c^B$, $\pi(f^A(\bar a))=f^B(\pi\bar a)$, and $A\models R(\bar a)$ if and only if $B\models R(\pi\bar a)$. Injectivity handles <logical equality>. Equivalently it is an <isomorphism of structures>[isomorphism] onto an $L$-substructure of $B$, or a map preserving the truth of all <quantifier-free formulas>. Preserving relations in only one direction would instead give a weaker homomorphism notion, not an <structure embedding>[embedding].
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