@Christine ******
Again, does your son travel with one or two passports? If one I can see that something was achieved in the transfer (although still doubt it is in fact possible to do). If he still has to travel with two passports then concerning the visa, I don't see what has been achieved.
Is it possible that you are confusing information about the visa, rather than the visa itself?
I'm looking at my new passport, specifically the first two pages. I had immigration transfer my extension of stay from the old to the new passport. In addition, there is a stamp stating when my last Thai visa was issued (years and years ago, not even close to being valid). Also, the entry stamp when I was admitted to Thailand under that long ago expired visa. My extension of stay, of course. And finally, the entry stamp when I was admitted to Thailand under that latest extension of stay.
If I wanted to actually use that visa (which of course, I could not as it expired many years ago) I would have had to travel with my previous passport which contained the original visa, but only while it was unexpired.
When a visa is issued it is put into your current passport and remains there. It does not get transferred to your new passport. While it is still valid you can use it in conjunction with your current passport. Once your visa expires, of course, you no longer need to carry your previous passport.
I think if your son (or anyone else for that matter) tried to use the visa that is referenced in your new passport rather than the actual visa that exists in your previous invalidated passport, he would not be successful. Immigration would demand to see the original visa in the previous passport. Therefore, he would need to carry both his previous and current passports. The notation in your son's new passport does not constitute a valid visa. That valid visa exists in his previous (invalidated) passport. The previous passport has been invalidated (e.g., punched or corner cut off), but any valid visas can still be used until they expire.
The extension of stay that was transferred to my new passport is in fact of equivalent status to my extension of stay in my old passport. In that sense, it can be said to be transferred. I do not need to carry my old passport to show anyone my original extension of stay. That is not the case with visas. With visas, you have to carry your old passport with a currently valid visa until that visa is no longer valid. It is not enough to carry your new passport if you are relying on an unexpired visa in your old passport.