I need to know!

Hello. I have a small question that needs clarifying. When your navi takes damage in battle, when the battle ends and you jack out does the hp of the navi go back up to full? If not then how, when or where do you replenish it?
If you jack out, your navi recovers to full hp. If you continue to battle without jacking out, your hp stays the same as at the end of the battle.
thanks a lot.
HealProgs in the PET.