You need a pre-departure test - within 3 days of departure of vaccinated and within 1 day if not. You need copies of vaccination status (if vaccinated) and a copy of your test results. Depending on what airline he is flying out on, he may be able to upload these on the Verifly app - I flew on BA, which partners with this app, UK-US last week - you can check in online if the docs are uploaded there (allow 4 hours or so from time of upload) otherwise you need to check in at the airport and supply copies there.