Traveling
 

Had this happen in a men's league game.

I was working with a less-experienced official. I was trail and he was lead. A1 made a shot that didn't hit the rim or backboard and he got the rebound. My partner (lead) called a travel.

I know this is a travel in the NBA, but I'm pretty sure that it's legal for high school and college. Unfortunately, I think most beginning officials get their education from watching the NBA, me included when I first started.

Can I correct the call and award the ball to team A?

What if it happened in a real HS basketball game?

If the player attempts a shot(in the officials judgement):) there is no travelling.

The key is attempt. An attempt to score does not have to touch anything.

While you cannot correct your partner on a judgment call, you should bring it to your partner's attention if he is misapplying a rule.
During that dead ball you should come together discuss the call and get it right. Allow the official who made the original call to make the correction.

BTW you are exactly right about this call. It is a travel in the NBA, but is a legal play in NFHS and NCAA.

The NFHS rules reference is case book play 4.44SitB, if you want to look it up. My NCAA book is in the attic, but it's the same ruling as NFHS.