Well, I think I've found the solution for this problem:
1. Copy all textures used in the materials to the 'tex' folder in your own preset library. Even textures from other presets libraries.
2. Reasign textures from the library to the materials (all file paths should point to 'preset://your_library/tex/file.xxx')
3. If you use layered materials, add a Null object as the child of your model and assign to it layered materials and all materials used as layers (for example: layeredMat and Mat1, Mat2 etc.)
4. Drag your model to the preset library
5. Finally drag your model from your library to s new scene...everything should works fine :)
Point '3' also works well when copying model with layered materials to the another scene.