How are you backing them up on the old phone? If you are using an app, have you looked at what the developer recommended for restoring the messages?
I'm most definitely NOT a VZW employee. If a post answered your question, please mark it as the answer.
I actually use Verizon Messaging for my Texting App... you just select "Save Conversations" > "Filename:" and hit "Save". It saves a file and a folder to the "VZMessages" folder in External Memory. When I go to the new phone and hook it up to the PC, there is no "VZMessages" folder to place my old stuff in. I have the "VZW Messages" App installed and working on the new Maxx and I can do the "Save" function with that. It saves a similar file name but doesn't say WHERE it's saving it. There has to be some area of the new phone that is inaccessible to the PC's file manager, it seems.
Got it! I used "ES File Explorer" on the Razr Maxx as my file manager and loved it. I installed it on the new phone and it gives you access to much more of the phone than the PC connection does. I just pasted the file from the old phone into the newly FOUND VZMessages folder and it began the restore process immediately. It's funny, when I connect the old phone to the PC, it shows me to virtual drives and everything on them. The new phone does not do this! Thanks for the attempt...