H&M will recommend Leather Magic and Leather Masters (if the latter is still in business this month or you can figure out who the current owner of the brand would be).

I know the chemicals are stronger for finished leathers vs. aniline, hence the two different kits. The one for finished hides has to have more power to get through the topcoat. As to specifics how it does that, I don't know. You can call Leather Magic and they will explain it to you, I'm sure.