  The AGT relations reduce S-duality to the modular transformations of
conformal blocks. It was recently conjectured that for the four-point conformal
block the modular transform up to the non-perturbative contributions can be
written in form of the ordinary Fourier transform when
$\beta\equiv-\epsilon_1/\epsilon_2=1$. Here we extend this conjecture to
general values of $\epsilon_1,\epsilon_2$. Namely, we argue that for a properly
normalized four-point conformal block the S-duality is perturbatively given by
the Fourier transform for arbitrary values of the deformation parameters
$\epsilon_1,\epsilon_2$. The conjecture is based on explicit perturbative
computations in the first few orders of the string coupling constant
$g^2\equiv-\epsilon_1\epsilon_2$ and hypermultiplet masses.
