If you are a Verizon Samsung Galaxy S III owner and travel international pretty often, this guide we found should prove pretty useful to you. Because VZW included multiple radios, you can convert your VZW SGS3 into a world phone. We won't say it will be easy, because, as you can see below, the instructions are long. Still, if you follow them precisely, you can make your phone even more useful. It was developed by XDA member, lair12, and is much appreciated. Here's the breakdown below:
Before leaving the U.S., you need to complete the following:
  1. Root the phone with stock ROM
  2. Use sprint.recovery.image for clockworkmod (others may work as well)
  3. Load APN Manager app from Google Play
  4. Load HiAPN Global app from Google Play
  5. Load Ghost Commander app from Google Play
  6. Load Dropbox app from Google Play
  7. Load PhoneInfo app from Google Play
  8. Back up APN’s to sd card through HiAPN
  9. Edit “apnlist_backup.xml” found at sdcard>HiDroid_Net>HiAPN using Ghost Commander app (select DB text editor to open) and then edit to include your required APN information. Here are two sites (option 1 and option 2) to check if you do not know the correct information. You can also load several options into the APN file data so you can be ready for several possible providers.
  10. Use HiAPN to restore APN’s
  11. Use APN Manger to see APN list and check that info for new APN is correct (APN manager cannot do anything else or it will crash)
  12. Use APN Manager to check to make sure that APN for now is still set to LTE-Verizon Internet or EHRPD – Verizon Internet

Once overseas, you need to complete the following:
  1. Turn off phone and pull battery and put in micro SIM from your foreign country (I’m using MTS in Russia, but was prepared for several other providers)
  2. Turn phone back on
  3. Turn off wifi
  4. Use PhoneInfo app to change preferred network type “Global” (click on Device information and scroll down for first box to change).
  5. Open HiAPN and select “Click to Autoset APN’s” or hit “Net” one change at a time until you rotate to the correct APN
  6. Go to airplane mode for a minute (this helps reset the radio)
  7. Take off airplane mode
  8. Go to Settings>More Setting>Mobile Network and make sure that is not grayed out. If not there, try going back to HiAPN and doing the “Net” cycle again.
  9. Check Settings>More Settings>Mobile Network>Access Point Names to make sure correct APN is selected. (If not, go back to step 5).
  10. Reboot phone, you should have the cars working.

Once back in the states, complete these steps:
  1. Use Phone Info app to change preferred network to “LTE/CDMA/EvDo”
  2. Pull battery and put Verizon LTE micro SIM card back in
  3. Power up phone
  4. Turn off wi-fi
  5. Open HiAPN and hit “Net” one change at a time until you rotate to VZWINTERNET
  6. Use APN Manager to check to see if it is set to LTE-Verizon Internet or EHRPD – Verizon Internet
  7. Check Settings>More Settings>Mobile Network>Access Point Names to make sure correct APN is selected. (If not, go back to step 5).

If for whatever reason these steps fail (Once back in the states), then do the following:
  1. Reset phone to non-rooted stock, Go here for more info.
  2. Do full phone reset,
  3. Re-root
  4. Re-clockworkmod
  5. Restore ROM through recovery mode.
This has been tested in Russia, so it is known to work. Let us know how it goes for you if you have the need to use it.

Source: TalkAndroid