The Google Play Store identifies you as a customer via your Google account (not via your phone number or some other phone ID). You may install 3GW on several phones, move it from one phone to the other, or change SIM (thus phone number), provided you use the same Google account as the one you used to purchase the application.
If you reset the phone / upgrade your OS or flash a ROM, you must set up again this account (as the main/first account) on the phone, or the Google license checking server will reject you. Make sure you have an active Internet connection when you start 3GW for the first time after that.
See also Google’s help article http://support.google.com/googleplay/bin/answer.py?hl=en&topic=1100168&ctx=topic&answer=113410.