I played as Serena, and the spells only appeared in the spellbook for the duration of the battle.
Yes, yesterday we played on the fresh mod 3.0 - Eagle Eye granted spells during the battle, but after the battle, they disappeared from the spellbook, according to him.
I'm attaching the save files; we played without passwords:
https://dropmefiles.com/P6pva
Thank you for the information. However, so far, I've only been able to reproduce the following situation:
1. Attack a hero with Eagle Eye.
2. Cast a spell.
3. The hero with Eagle Eye learns the spell.
4. Flee.
5. The learned spell is not in the spellbook.
6. Pass the turn.
7. The learned spell appears in the spellbook.
Can you verify if this is what happens in your case?