"And the LORD God formed man [of] the dust of the ground, and breathed into his nostrils the breath of life; and man became a living soul." Gen 2:7, KJV
So man doesn't have a soul, he is a soul; a physical being.
It doesn't live on in an 'afterlife', it dies because of sin.
"Behold, all souls are mine; as the soul of the father, so also the soul of the son is mine: the soul that sinneth, it shall die." Ezek 18:4
The non-Biblical religions created the soul- a 'core part of man that doesn't die'. It's useful in recruiting, if you convince the acolyte that his core part will be punished eternally if the group's rules and rulers are disobeyed. The Bible OTOH presents one punishment for sin: death, not 'life in eternity'. Romans 6:7,23. And that punishment is for disobeying the Ruler and his Rules.
Hawking, like so many others, has picked up the popular wisdom without checking the sources for himself. "Shoemaker, stick to thy last."
He does have one thing right: The computer/man/body/soul stops working after a while (if war, disease, or accident don't interfere). Resurrection, another topic entirely, is the only 'cure' for death.