The material favorites are stored in the %appdata%-area of a users local machine. When a user selects a material from a material library as a favorite, a copy of that material is stored in the favorite materials library.
On change of the material in the original library, there is no notification, that the favorite-material might be outdated, nor an easy way to update that modified material in the library to the material favorites.
Both would be appreciated.
Maybe one way could be, that on startup Inventor checks if the materials in the favorites library are still valid according to the materials-library they are derived from.