Woodin's Ultimate-L conjecture that Ultimate-L implies the Extender Embedding Axiom

Let $\mathrm{EEA}$ denote the Extender Embedding Axiom, and let $V=\mathrm{Ultimate-}L$ denote the corresponding Ultimate-$L$ axiom. Woodin's Ultimate-$L$ conjecture. The theory

$$\mathrm{ZFC}+V=\mathrm{Ultimate-}L$$

proves $\mathrm{EEA}$. This is an inner-model-theoretic prediction about the Ultimate-$L$ program; the source presents the implication as a conjecture, and its resolution is not specified here.