No, they have different soul because they have different Consciousness. Here is passage from Aitreya Upanishad showing it:
III-i-3: This One is Brahman; this is Indra, this is Prajapati; this is all these gods; and this is these five elements, viz. earth, air, space, water, fire; and this is all these (big creatures), together with the small ones, that are the procreators of others and referable in pairs to wit, those that are born of eggs, of wombs, of moisture of the
earth, viz. horses, cattle, men, elephants, and all the creatures that there are which move or fly and those which do not move. All these have Consciousness as the giver of their reality; all these are impelled by Consciousness; the universe has Consciousness as its eye and
Consciousness is its end. Consciousness is Brahman.
III-i-4: Through this Self that is Consciousness, he ascended higher up from this world, and getting all desires fulfilled in that heavenly world, he became immortal, he became immortal.
First Sutra of Shiva Sutras also state 'Chaitanyam Atman' or 'Consciousness is the self.'