This is a general tutorial to get the Verizon Samsung Galaxy S4 to work on GSM networks. We're basically doing the same thing to get it on AIO Wireless. The source of this information is lair12 @ XDA. I don't have a Verizon S3 in my possession anymore.
I've posted the information from 106 below this and my comments about the use of CM below that.
Using Samsung Galaxy as World Phone (stock ROM)
Go to PAGE 11, POST #106 to see a simplified method. If this works well, please reply with your results in this thread.
I have had success with my SGS3 in the following places:
UK using Vodaphone
Rome using TIM
Morocco using Maroc Telecom
Russia using MTC
Finland using DNA
India using Vodaphone
Nepal using Ncell
My Phone: Verizon Galaxy S3, rooted with stock ROM and with Sprint version of custom recovery (other ROM's and recoveries may work as well.)
Preliminary steps that were done before leaving the US:
a1 – From Google Play store install the following apps if you do not have them: APN Manager Pro (81 Square), HiAPN Global (install as a system program when it asks), ES File Explorer, Dropbox, Phone Info (sc@taiwan), Titanium Backup and Open Signal Maps.
a2 –Backup your phone app: com.android.phone with Titanium Backup. (I suggest you do a full backup of all apps and data as long as you are doing this).
a3 – Open HiApn Global and back up APN's to sd card: HiAPN Global>Click to Backup APNs (this will create a file named “apnlist_backup.xml” on your internal SD card at /sdcard/HiDroid_Net/HiAPN).
a4 – Open ES File Explorer, then go to menu>settings