When I receive voice messages on my new iPhone 4S (using Verizon services) , is there a way of
copying/moving the voice message from the Verizon voice mailbox to my iPhone (and then to my mac?)
Nope, Unless you just play your Voicemails on speaker phone and record them with your mac
Verizon offers a service (through a 3rd party and it's not cheap) to have your voicemail messages archived. I believe that you can then download them or have them sent to you on disk. Repeat: it's not cheap.
Retrieving data ...