Let $\delta$ be a limit ordinal and consider an elementary embedding $j:V_\delta\prec V_\delta$. We define $j^+:V_{\delta+1}\to V_{\delta+1}$ by setting, for $R\subseteq V_\delta$, $$j^+(R)=\bigcup_{\alpha<\delta}j(R\cap V_\alpha),$$ note that $j^+$ is not necessarily an elementary embedding.
Given $j,k:V_\delta\prec V_\delta$ exercise 24.5 in Kanamori's The Higher Infinite asks to prove that $j^+(k)$ is also an elementary embedding of $V_\delta$ in itself and that $\mathrm{crit}(j^+(k))=j(\mathrm{crit}(k))$. The hint given to show elementarity is to "replace quantifiers with Skolem functions and use a reflection argument".
I know little about Skolem functions (essentially what's said about them in §3.3 of Chang-Keisler) and all I know about reflection is the Lévy-Montague reflection principle, so I could use a sketched solution or a more extensive hint, I'm finding it hard to think about $j^+(k)$ and show its elementarity even for quantifiers-free formulas