It has been 11 years since I had to do this, when I started to receive a UK pension and HMRC began taking payments under PAYE. I was a US resident at the time. It was definitely form 2002 that I completed and sent to the IRS and within a couple of months my tax code was changed to NT and I received a refund for the 2 months PAYE tax that had been paid.
Hopefully someone will come along shortly with a more recent experience.