I think WA is a state contact for handgun purchases... but not totally sure.
I was denied once as a result of an NICS check for a handgun run through the FBI. I appealed it and had it reversed. In my case, it wasn't mistaken identity, just that the examiner in VA didn't bother to look at what I had on my record to see that it was a misdemeanor little thing, not a felony. Probably just a lazy government worker thinking i wouldn't fight it.. oh well, that's long over with... that started my hatred for the NICS and the government in general... needless to say, I now have way more evil stuff than I ever would have had they not been so stupid.
As far as your friend goes.. he may not want to tell you... make sure he knows the prohibitive criteria first off.
If he appeals through your state or the FBI, it will involve at least the following steps.
Get the contact information from the dealer who denied him... they should have a pamphlet or at least direct him to the right website.
Requesting reason for the denial from the agency that denied you. NICS accepts emails, WA state may as well.
Submission of fingerprints for verification of identity.
They will respond and tell your friend that they either made a mistake or it stands that he's denied.
If it stands, your friend must provide court documentation disputing what they have on record from him. This can usually be accomplished by calling the courthouse that they have on record as issuing a prohibitive judgement and getting certified copies of the court documents... in my case, it cost like 7 bucks. Then, mail these (providing they show you shouldn't be denied) to the agency that denied you, and they'll reverse it... if all goes well.
Of course, and I hate to use myself as an example... this will continue to happen over and over again unless that actual agency that provided the bad records corrects them. This is difficult to make happen, I'm STILL working on it. What your friend can do, if he appeals sucessfully, is enter into the VAF that I have in my sig line, or if it's through a state authority, whatever they have... that should clear up the delays/denials but will still flag if you get run for other stuff... cough, C&R, cough
The whole deal took 4 months for me to clear up with NICS. If you have specific questions you can also PM me... I know all about the NICS appeal process... or else just ask here, I'm sure I'm not the only one who has been denied... the gov makes mistakes... a lot actually... ~1/4th of appeals submitted turn out to be mistakes...