New telephone installed. - Recording inoperative

I have just replaced my old phones with a new phone.  However, people calling me and leaving a message, still hears my former greeting and records on my old phone.   At least the people calling in hear the recording and believe they have recorded a message.  My new phone does not record, although the greeting is on the new phone, the new phone menu  indicates that the it can receive and record messages.  But when I call on an outside phone to retrieve my messages, I can hear the messages, but they do not record on the new phone.  How to fix????  Am I to notify Verizon of my new phone?