How does training inheritance work?

Training is never wasted while you stay inside one family, so you can invest in whatever you have now. Training spends resources to raise a creature's individual potential stats and combat power. If a better copy turns up later, the levels and stats you built move across to it, and you do not pay for them a second time.

The new holder does not have to be the same creature, and it does not have to be at the same stage. You can move training from an evolved Aniimo back onto a lower evolution stage of the same line. The one hard limit is family. Training cannot cross into an unrelated creature, so committing resources to one line is still a real choice.

Evolution is a separate bill. Evolving an Aniimo costs its own materials, evolution stones among them, and nothing here says inheritance covers those. If you move training onto a lower stage, plan on paying for that creature's evolutions yourself.

Not settled: The game describes the system both as working within a family and as transferring between creatures of the same species. Moving training between different evolution stages is supported. What happens with branching lines, where one family splits into different evolutions, is not settled.