How do I flash a Samsung device using the distribution on samsung-updates.com?
Is SPR-L720VPUEMJA-20131030154609.zip stock ROM? If yes, you can use the Odin tool to flash that ROM.

I assume have already installed Samsung Kies (so phone drivers are installed). With this done, open Odin (don't change any settings). Load L720VPUEMJA_L720SPTEMJA_L720VPUEMJA_HOME.tar.md5 into the PDA section into the ROM. Put your phone into Download Mode (Vol Down + Home + Power), and plug it into Odin. Odin should be able to detect that phone. When it does, start the flashing process.