In the scope of rigorous sensor fusion in kinematic laser scanning, we present a qualitative improvement of an automated retrieval method of lidar-to-lidar 3D correspondences in terms of accuracy and speed, where correspondences are locally refined shifts derived from learning based descriptors matching. These improvements are shared through an open implementation. We evaluate their impact in three, fundamentally different laser scanning scenarios (sensors and platforms) without adaptation: airborne (helicopter), mobile (car) and handheld (without GNSS). The impact of precise correspondences improves the point cloud georeferencing/registration 2 to 10 times with respect to previously described and/or industrial standards, depending on the setup, without adaptation to a particular scenario. This represents a potential to enhance the accuracy and reliability of kinematic laser scanning in different environments, whether satellite positioning is available or not, and irrespectively of the nature of the lidars (i.e. including single-beam linear or oscillating sensors).