Calculating an in-loop signal as part of a hierarchical control loop
UPDATE: My original answer incorrectly assumed the outer loop would not impact the result, but as pointed by Ben, this transfer function is dependent on the fast feedback. 

The resulting equations are found by solving for $A/X$ from the block diagram below, with X representing the disturbance input:



Solving this:

$$Y = P(SY+FY+X)$$
$$A/S = P(A + FA/S + X)$$
$$A = PAS + PFA + PXS$$
$$A(1- PS - PF) = PXS$$

$$\frac{A}{X} = \frac{PS}{1-PS-PF}$$

Note that this follows the general equation for the closed loop gain using:

$$G_{CL} = \frac{G_F}{1+ G_{OL}}$$

Where:

$G_{CL}$: Closed Loop Gain

$G_{F}$: Forward Gain (In this case $G_{F}  = PS$)

$G_{OL}$: Open Loop Gain (In this case $G_{OL} = -P(S+F)$

Note how negative feedback is assumed in the generic expression, but since the block diagram does not show negation at the summations, the open loop gain is then negative as given above. Using the general equation and recognizing that the parallel result of S and F as a gain given as S+F allows us to solve this from inspection.