If you plan to record a phone call, you must first ask whether the law requires that you obtain consent from one or all of the parties to the call before recording it. Federal law permits recording telephone calls with the consent of at least one of the parties. See 18 U.S.C. 2511(2)(d). Many state wiretapping statutes also permit recording if one party to the phone call consents, while other states require that all parties to the communication consent.
It does not appear that there is a rule or opinion on point under the circumstances in question. Therefore, it is probably best that you obtain the consent of all parties before recording in order to avoid any legal liability. For more details on federal and state wiretapping laws, see the Recording Phone Calls and Conversations section of the CMLP's Legal Guide.