Why are you paying this at all? Dispute it with the credit bureaus as a victim of fraud. You may have to file a police report about it. Tell the military the truth about the situation instead of trying to take responsibility for something you didn't do.
As for how long it takes Synchrony to clear the debt, that's an internal issue and there's nothing you can do to speed it up. You could pay by check and once the check clears your bank, you can show that as proof to the recruiter that it's been paid. Make sure you send the payment via certified mail and keep the tracking number for your records. You can also show this to the recruiter along with the cashed check. The sooner you do it, the sooner it will get done.
“Faith is taking the first step even when you don’t see the whole staircase.”
