Well, sort of... If your talking voice mails, that is done with Verizon, call into your voice mail, go to advanced option in the voice menu, and there is an option to SEND an voice mail or forward. Love this one, when I am really ticked off at my wife and I DONT want to talk to her but, I want to say something. I use this, You can start a new voice message and send it directly to them.
There is an option after listening to FORWARD to another number (think this only works with Verizon customers)
If you get a text message you want to "forward" to someone else, you CAN hold the text, the menu will come up, COPY, create a new text message to the one you want to send it to, and when the keyboard comes up, just select the paste.
Not a true forward for text messages but, it does work in a pinch.
Of course if your trying to move to another phone, Verizon backs up 90 days of text messages, so if you get a new phone before you do anything on the phone, in one of the menus (saw this in Android), select the option to restore messages.