This can be done fairly easily provided your modem supports it. In addition
to what Carey said about recording phone conversations being illegal without
the consent of all parties involved, you should be aware that if you record
the conversations yourself, they will be 100% inadmissible as evidence in
court because the validity and the chain of possession cannot be verified.
Some states allow an exclusion for answering machine tapes. You could
contact a lawyer before proceeding, as you could set yourself up for
litigation without finding out what is legal in your jurisdiction.
Bobby