Just a quick note regarding Ivory. I have had a set of billiard balls still in their original wooden box that contained a label on how to care for the elephant ivory balls. The recommended preserving agent for cleaning was sperm whale oil.
Years back I bought this oil from Dixie Gun Works , but I have no present source. This is for your information only and I am not trying to recommend any specific care or use. The OP indicated that her sister has the missing piece of the stock. A good conservator may be able to rejoin the two in a proper manner.