Thanks for the detailed steps. The step for "Call National Insurance" is problematic. Not everyone there appears to know the specific department that handles US citizens living in the UK and working self-employed. The "International Caseworker department" may be some help (my son is trying it now), but I'm worried about him getting directed to the path for UK citizens who plan to work in the US, instead of the reverse. The instructions posted on the ssa.gov site (https://www.ssa.gov/pubs/EN-05-10199.pdf, bottom of page 4) tells US citizens self-employed in the UK to send a letter requesting the Certificate of Coverage to an Inland Revenue office in Newcastle upon Tyne, but perversely, the text around that address indicates it's for those living outside the UK. (!) The guidance on page 10 for those living in the UK is "contact your nearest office of the Department for Work and Pensions." That doesn't work at all. Contacting HMRC resulted in a copy of his National Insurance Record (list of annual payments to National Insurance since 2009), which should be proof enough, but I suspect the IRS will bounce that and require a Certificate of Coverage instead. This is ridiculously difficult.
