Evolving after skill lvl up?

Hi, I started the game a couple of days ago.
Awesome new website for an awesome game.

I was wondering what happens when I evolve my luffy after leveling up his skill.
Does the reduction in cooldown pass on to the next form?
Or only half of the effect pass on like brave frontier?

It will all transfer IF the Special Move name is the same.

If the Special Move is different, all levels will be lost.

Oh, then I should save some of luffy's skill book for later.

Thank you.

Huh, seems like there's a book for each different skills.
Would be meaningless to save Luffy's bazooka skill book for later.