Parameter extraction from DFT results, possibly with leakage effects
Interpolation is one method used to estimate parameters of non-periodic-in-FFT-aperture signals.  Parabolic or, better yet, Sinc interpolation will help with estimating both the frequency and the amplitude peak B.  For phase interpolation, I find it easier to use something like a pre or post fftshift to move the phase 0 reference to the middle of your data, then interpolating an estimated phase from the fft, then offsetting the phase back relative to wherever using the frequency estimate.