To encode a signal $x_m$ in a carrier with frequency $f_c$, we proceed as:
y(t) = \cos(\phi(t)), \\
\phi(t) = 2\pi \cdot \left(f_c t + f_\Delta \int_0^t x_m(\tau)d\tau \right)
where $f_\Delta$ controls the maximum deviation of $y$'s instantaneous frequency from $f_c$ (effectively its bandwidth, but not in strict Fourier sense).
The magnitude of the FFT will likely scale by the number of samples N depending on the specific algorithm you use. So the IFFF will be 1/N. Just multiply your FFT bins by N to normalize it. If you use any windowing this will change the result accordingly