Deriving Fourier transform of auto correlation function from probability distribution

I am self studying a book "Neuronal Dynamics" https://neuronaldynamics.epfl.ch/online/index.html

And I found this very challenging to derive this from p_0

https://neuronaldynamics.epfl.ch/online/Ch7.S5.html#Ch7.E45

Until (7.37) was OK, but after that seems really difficult.

Anyone knows how this equation is derived?