If a POG, awarded with a CAB (combat action badge), were to transfer to Infantry, would the soldier be authorized to wear the CIB?

No the CIB is based on your MOS at the date and time the citation was awarded. You would be a new infantry soldier with a CAB.

I was AF, but as far as I understand, all badges are earned. No trades involved. How did this soldier get promoted to Spec 4? Why wouldn't he ask his Sgt., if he didn't know?

A medal earned is a medal worn. When joined the ARNG in the late 60's, an inspecting Major asked what were the medals for. A GCM and NDM????? If it was today, I would have told him, I got them for failing to beat the draft.

I think most soldiers realize that if an award isn't annotated in your IPERMS file you are not eligible to display it. For years I had a foreign award that wasn't in my files so thus did not wear it until this was corrected.

No. While in Iraq my convoy was fired at and everyone jn my CET got a CAB except 1 guy who had an Infantry MOS he was awarded the CIB.

First of all a POG is a derogatory disgraceful thing to call a fellow Soldier!

Why embarrass yourself by asking such a silly and disrespectful question on a public website? When you could have simply asked your NCO. Probably because you knew you would be doing push-ups till kingdom come if your NCO had any worth. "POG's" are the ones that feed you. Get you the supplies needed for you to fight. Drag your injured or dead body off the battle field. Fly the helicopters to drop you into the battle, or to bring you back to save your life.
Or in my case for the majority of my career, fix your vehicles and recover them when they are broke down or blown up. And in case you haven't thought it through, as you seem to have a habit of, the enemy knows the vehicles will be recovered. I will let you finish this thought on your own. I completed four deployments, my first being the invasion of Iraq. I don't see a V next to your name, so I imagine you as more of a "POG" then I am. As I am someone who has been mortared more times than I can count; been fired at by bullets that were not blanks and returned fire; and by God's grace with as many recovery missions as I completed, only had my vehicle blown up under me once.
Now would be a good time to learn some respect for the majority of the army. First by eliminating the term POG from your vocabulary.
To answer your question, no, we do not wear the CIB unless our MOS is infantry. Someone wiser than you decided that we should receive an award in recognition of our service and sacrifice's. Your Infantry brother's deserve their award, we deserve ours.

What the hell is a CAB? Like a participation trophy for little league?

Why not if you earned it wear it. Semper Fi

Absolutely not