Yeah, the local head of the PD.
With so many towns and villages thousands of miles apart, you just use the local office or ASP if needed. The dealer holding the NFA item should be familiar with this unless it's his first try.
Any time I have used SS they have sent my dealer all the info, the transfer, and fees for this ahead of me even knowing it. My dealer has the fingerprint cards set out and an appointment with the LEO for the task. You or your friend should not have to work for any of this at all.
And yes, SS pays the transfer fees to the dealer so they do not need to collect from the end user.