Well, they will need positive evidence that your Mother stole the items if they were going to prosecute.
You can consider writing the letter stating that she has not stolen anything from anyone ever. That she does not have the jewelery nor any knowledge as to where the belongings are. You can consider mentioning that she has never have anyone in the residence without owner consent. And, also that there have been "random" workers in the apartment recently. You can give specific time frames, if she can recall when and who.
You can consider stating that she is offended and emotionally distraught with hurt that after 15 years they suspect her of being so disloyal as to be a thief.
If she wants to resign, then she can add that the letter should be consider an immediate resignation as she does not want to work for any employer who has such trust problems.
Now, on a side note, many times, these people steal from themselves. They pawn the property to get money and then try to claim it on their home owners insurance. So this could very well be an insurance scam and they need to put focus on someone.
Once she resigns, their attorney may turn the matter over to the police for investigation. Keep in mind, that your Mother does not have to participate in any investigation without the presence of an attorney. So if she gets contacted by the police, she really needs to consider consulting with a local attorney to be there with her.