WellÂ… I dont know. What is a soul, right?
The Phoenix Force copied something about Jean. Her memories, her essence…. something. We don’t know exactly what it was because different writers have approached it differently. But whatever it was, the Force tried to return it to Jean.
Now, Jean wasnÂ’t lacking part of her soul/essence/whatever-that-was: the Phoenix had copied it. But the original Jean was still whole, unconscious while her body healed the wounds of the radiation at the bottom of Jamaica bay.
Once the copy of JeanÂ’s body died in the Moon, that copy of her essence/soul was supposed to be re-integrated/merged with the original (who was inside the healing cocoon). So it went back to Jean.
But original Jean rejected it because that copy of hers brought the memories of what she had done as Phoenix - killing an entire star system. So that Phoenix fragment, which was carrying that copy, found another Jean - the un-animated body of Madelyne Pryor - and it returned JeanÂ’s soul/essence/memories/whatever-it-was to that body, animating it to life.
So Madelyne isn’t just a clone (a genetic copy) of Jean. She’s more than that.
And in case you’re wondering, yes: that fragment remained with Madelyne the whole time and goes back to Jean, choosing her, saving her from Madelyne as they fight during Inferno. That same fragment remains with Jean until Morrison’s run.