Hey, thecooks! This is a great question. If the credits you're receiving for your son's phone are from the September 2016 iPhone Trade-Up offer, then I found this gem of truth in our internal document for that promotion:
If customers want to upgrade a line receiving promotional EIP bill credits and keep the credits, they can perform a standard upgrade with or without EIP to a new device. Customers can pay of their qualifying EIP and continue to receive the bill credits at the account level. If they JUMP! to a new device, they will lose the credit.
In this situation, since you're thinking of paying off the remaining EIP balance for his device and THEN completing an EIP for a new phone using the old phone as a trade-in, you should actually be able to take advantage of both promotions. The credits for the iPhone 7 will continue being issued at the *account* level, and you can trade the phone in once it's paid off to qualify for the Q4 $300 iPhone offer and get credits fior the iPhone X at the EIP level.
I double checked the Q4 internal offer content and found the exact question there too --
Q: If I pay off my iPhone 7 and am still receiving credits for the September iPhone 7 Trade-up offer, can I use the iPhone 7 for the $300 Q4 iPhone offer on the iPhone X?
A: Yes, this would work fine as those credits will now be at the account level due to the device being paid off.
Edited to add: The order of operations here is pretty important! I wanted to call out that a trade-in has to be completed at the time of the upgrade, so you'd need to pay the iPhone 7 off first in order for it to be eligible to trade-in during the order for the iPhone X. Just rereading my original reply and I'm not sure if I made that clear!