Russell's argument for the mind being created by the brain

Bertrand Russell (a famous 20th Century philosopher) once said:

"The mind grows like the body; like the body it inherits characteristics from both parents; it is affected by disease of the body and by drugs; it is intimately connected with the brain. There is no scientific reason to suppose that after death the mind or soul acquires an independence of the brain which it never had in life".

Something can be dependent on something else without being created by that something else.  For example, when someone is in a building their ability to see the sky is dependent on windows and the glass in them being relatively clean and so on. But such a dependence only applies when inside the building.  It doesn't depend on the window if they were to venture outside.  Their view of the sky would be, if anything, enhanced.

So Russell needs to say more to justify that the mind or soul couldn't have such an independence.  The mind-body correlations are insufficient in themselves to establish there is no afterlife.