Left transiter of ideal is derivation-invariant Lie subring

ANALOGY: This is an analogue in Lie rings of a fact encountered in group. The old fact is: left transiter of normal is characteristic.
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Statement

Suppose $L$ is a Lie ring and $A$ is a subring of $L$ such that, for any Lie ring $S$ such that $L$ is an ideal of $S$, $A$ is an ideal of $S$.