Is there any s/w that will make my Sprint Galaxy SIII a mobile router that works on O/S 4.1.1 Jellybean?

stock formware ... try wireless and network then tethering and portable hotspot in your settings that should (possibly) give you data hotspot via usb wif-fi or bluetooth no need for additional software (unless your carrier has disabled this)

If your phone does not have the option for a hotspot, try Wireless Tether for Root users. It can be found on the market and it's FREE!