Actually FEFF does not transform the LDOS into the final XAS spectrum. Although both the LDOS and the XAS are obtained
from matrix elements of a one-particle Green's function, they are obtained in FEFF from two different calculations: the
XAS is calculated in the presence of a core-hole, and the LDOS is obtained from the ground state without a core-hole..
This is explained in detail, for example, in Ankudinov, et al., Phys Rev. B 58, 7565 (1998) as summarized in their Eq. (1):
As a consequence the LDOS and the XAS are not directly related. Indeed, as pointed out in the above reference: