Yes they do have the same soul because it’s the same soul that's reincarnated as Kagome, when Kikyo died in the end for good her undead self ceased to exist, any reference to her moving on to the afterlife was a flaw in the story telling, touching though it may be. Kikyo even sad this herself in the beginning when she was brought back to life that if she were to die she would cease to exist forever. Inuyasha would see Kagome, the same soul in the form of its most recent reincarnation. And once it is reincarnated again he would see someone else, and Kagome would disappear (figuratively speaking).
The only reason Kikyo was resurrected as Kikyo when Ursue brought her back to life was because of the essence of her being left behind in the ashes and grave yard soil that was used in her resurrection, that combined with the lingering memories of her soul that was stored in Kagome’s subconscious.
Technically when a soul is reincarnated the entity of the previous life doesn't entirely disappear it just gets stored in the subconscious when reborn, that is how people can have innate abilities and such, from kills that surface from the subconscious mind from having been learned or mastered in a former life. Well this is my belief anyway.
kagome and kikyo dont have the EXACT same soul. if you think about it, they are two ENTIRELY different people. kagome is just the reincarnation of kikyo. they dont have the same soul... i think. but who would he see in the after life? i have no clue XD
