A never ending bug still existing ... as mentionned on SL wiki (https://wiki.secondlife.com/wiki/LlSetTextureAnim) :
Texture animation is a property of the prim (i.e., you can remove the script that started the animation, and the prim will remember the settings anyway.) Note, though, that as of Jan 2009, texture animation is still one of the prim properties that is lost when using the rezzed in world copy method of shift-drag.
Originally brought up in VWR-640, it got its own issue in SVC-3925"