You can firstly get your text messages from your old phone to your computer, then copy them from your pc to your new phone, this can all be done by using iPubsoft Android Desktop Manager, now have a look at this guide here: http://is.gd/MmGlUi
You can transfer text messages from an old phone to a new phone by having the text messages saved to your SIM card. Most text messages are saved to the phone, which is why they normally don't transfer when you put your SIM card in another phone.
To transfer text messages from an old Android phone to a new Android/iPhone/Symbian in a safe and secure way, please visit http://goo.gl/aV0hTn to read the detailed steps. Besides, it lets you do the task easily and convenient.