Fourier lightfield microscopy (FLMic) is a powerful technique to record 3D images of thick dynamic samples. Belonging FLMic to the general class of computational imaging techniques, its efficiency is determined by several factors, like the optical system, the calibration process, the reconstruction algorithm, or the computation architecture. In the case of FLMic the calibration and the reconstruction algorithm should be fully adapted to the singular features of the technique. To this end, and concerning the reconstruction, we discard the use of experimental PSFs, and propose the use of a synthetic one, which is calculated on the basis of paraxial optics and taking into account the equal influence of diffraction and pixelation. Using this quite simple PSF, performing the adequate calibration and finally implementing the algorithm in GPU, we demonstrate here the possibility of obtaining 3D images with good results in terms of resolution and strong improvement in terms of computation time. In summary, and aiming to accelerate the widespread of FLMic among microscopy users and researchers, we are proposing a fast protocol fully adapted to FLMic and that is very flexible and robust against any slight misalignment or against the change of any optical element.