Can I Upgrade To Specific Android Version?

[AC Question]

So, my LG Optimus G E970, which I got almost four years ago, started giving out. Volume Up button didn't respond, the lock button worked about a quarter of the time, and then a big portion of the screen became unresponsive to touch. So I bought another one of these phones, one that was refurbished. Here's the issue. My original was running Android 4.1.2, and I rooted it. I love this Android version, but the new phone is running Android 4.0.4. So, my question is, is there any way I can specifically upgrade to Android 4.1.2? Any help is appreciated.