Not quite...
https://www.learnreligions.com/reincarnation-in-buddhism-449994
What Is the Self?
The Buddha taught that what we think of as our "self"--our ego, self-consciousness, and personality -- is a creation of the skandhas.
Very simply, our bodies, physical and emotional sensations, conceptualizations, ideas and beliefs, and consciousness work together to create the illusion of a permanent, distinctive "me."
The Buddha said, “Oh, Bhikshu, every moment you are born, decay, and die.”
He meant that in every moment, the illusion of "me" renews itself.
Not only is nothing carried over from one life to the next; nothing is carried over from one moment to the next.
This is not to say that "we" do not exist--but that there is no permanent, unchanging "me," but rather that we are redefined in every moment by shifting impermanent conditions.
Suffering and dissatisfaction occur when we cling to desire for an unchanging and permanent self that is impossible and illusory. And release from that suffering requires no longer clinging to the illusion.
My qualm with Buddhism is this idea that the soul after death doesn't change.
Literally EVERYTHING MUST CHANGE. Including any souls and deities!
Otherwise there's no balance between life and after death.
Change is THE essential commonality between the two.
Without change there is nothing! Void! Like before the Big bang, where not even thought existed. Because thought IS change.
The balance IS CHANGE once again. There's Void and there is the balance CHANGE.
A permanent soul or personality will not survive death or spend anytime with a god or a devil.
The idea of God and the devil is supposed to indicate polarity in everything. Therefore balance is absent in Christianity.
I can't stress how wrong this polarity is. Because balance is absent.