
Quoting
pg1067
I'm sure the answer is yes. If your intent was to ask the folks who post here how your mother (a woman who is completely unknown to us) might identify the sender of an anonymous piece of mail, I hope it rather obvious that no one here will have the faintest clue (unless your mother wants to hire a private investigator or see if the police will take any interest in the matter, which they likely won't since it's not a criminal matter).
No one here can intelligently rule out the possibility, but she won't know unless she asks.
As mentioned, the police aren't likely to involve themselves. It's barely even a civil matter, and I wouldn't even expect the USPS to get involved unless the letter violates some postal regulation.
Defamation occurs when Person A makes a false statement of fact about Person B to at least one person other than Person B. The statement must harm Person B's reputation and, in general, must cause Person B actual monetary damage. The letter you described may have contained one or more false statements of fact about your mother, but the letter was (as far as you know) only sent to your mother. Therefore, it cannot give rise to a viable defamation claim by her (although the other people mentioned in the letter could, conceivably, have viable claims against the sender because the statements about them were made to your mother).