It seems to me that there is a difference between, say, the law of conservation of linear momentum or energy and the law of conservation of angular momentum. The first two are valid in any frame of reference and their invariance is a direct consequence of the relativity principle, whereas angular momentum may be conserved for observer 1 and not for observer 2, if they compute it around two different points (both observers are inertial). How can it be so? Is there a reason? And is it true that energy and momentum must be conserved for all inertial observers?