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Video stabilization is an in-camera processing commonly applied by modern acquisition devices. While significantly improving the visual quality of the resulting videos, it has been shown that such operation typically hinders the forensic analysis of video signals. In fact, the correct identification of the acquisition source usually based on Photo Response non-Uniformity (PRNU) is subject to the estimation of the transformation applied to each frame in the stabilization phase. A number of techniques have been proposed for dealing with this problem, which however typically suffer from a high computational burden due to the grid search in the space of inversion parameters. Our work attempts to alleviate these shortcomings by exploiting the parallelization capabilities of Graphics Processing Units (GPUs), typically used for deep learning applications, in the framework of stabilised frames inversion. Moreover, we propose to exploit SIFT features {to estimate the camera momentum and} %to identify less stabilized temporal segments, thus enabling a more accurate identification analysis, and to efficiently initialize the frame-wise parameter search of consecutive frames. Experiments on a consolidated benchmark dataset confirm the effectiveness of the proposed approach in reducing the required computational time and improving the source identification accuracy. {The code is available at \url{https://github.com/AMontiB/GPU-PRNU-SIFT}}.