Does the lithium, cobalt, etc. not undergo a material change as the battery is used? Meaning, is the lithium in a brand new battery the same as the lithium in a battery that's been used for years?
I would presume the question was about the physical and chemical state of the lithium rather than the atomic makeup. Like whether the lithium is ionized, whether it's a powder or crystallized solid, etc.
Both chemically combine with other atoms to form molecules - that is how a battery works. If they combine with the wrong thing it can be a lot harder to separate them again (not nuclear level, but harder)
The stoichiometry stays exactly the same, just shred the battery and feed the result back to the beginning of the e.g cobalt mining operation operation. Better however if you somehow manage to roughly separate it into lithium, cobalt and so on and use the result instead of the respective ore.