That explains things.
??
The Core Element explicitly contains one's will. It's straight-up stated as such. The Core Element is also stated to contain genetic code. The Jade Emperor's powers carried over to Mira via his genetic code, which INCLUDED R's soul and consciousness as R was able to talk to Mira through her having the Jade Emperor's cells.
Do these aspects not seem to connect to you in some way? Not even vaguely?
Being able to even copy someone's abilities in general, especially the Jade Emperor's Mind, which is explicitly stored within the Core (as in, its stores within conceptual information jargon) means its not standard Power Mimicry. Satan/Mujin aren't just copying abilities via standard skills, it's a conceptual ability.
Even further supported by the fact Satan was capable of yoinking his wings back from Mujin during their final battle. Which, we both agree, is a manifestation of Satan's own fundamental existence. The functions of the ability itself supercede the need for specific feats.