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Unless the allegations were proved to be done in a malicious manner they can not get that information because it is protected by privacy laws.
Most often these people are making threats to try and bluff the person into admitting it was them. The lawyer would have to petition the courts for the information and prove that the person did this in a malicious manner to inflict damages on his clients. Even then the judge will often not allow this information unless the person who called has done so repeatedly only to cause damages.