I have an Arduino Nano
We know what that is.
and GPRSBee_V1.2 module.
No clue. You need to provide a link.
I need to send an SMS with these two modules, is this possible?
If you connect them correctly, and write the right code, I can't see any reason why it shouldn't be. Easy is a different question.
I've tested with sample code does not work.
That's almost too lame to comment on. The code does something. You didn't explain what it does. You expect it to do something. You didn't explain what that is, either. All we can surmise from your comment is that the two things are not the same thing.