As long as your keeping the same number on the new cell the message would automatically go into the new phone.
You can transfer your messages by email. Just forward them to your email address. In the TO spot enter in your email address. In the actual text message the phone number,data & time will not be there. I suggest including that yourself if you want that info, then send.
Second option would be to use
BitPim software to transfer messages to your computer.
Thank you for your input Minniehaha!
In addition, please keep in mind that you must send your text messages to your email before you activate your new phone. Then, once you activate your new phone, you can send your text messages to your new phone from your email if you send to email@example.com, pictures can be sent to your phone as messages via email if you send your picture file at firstname.lastname@example.org.