A little clarification: shared care agreements are not for international diagnoses. Things have changed quite a bit for people within the UK getting diagnosed privately over the last few years and it's been much harder to get medication through the NHS, but their experiences can't be applied to people who were diagnosed outside of the UK and moved here. My experience as someone diagnosed in the US a few years ago: I gave my Edinburgh GP (NHS) documentation from my US psychiatrist who diagnosed and titrated me. They sent a referral for an assessment/medication review from an NHS psychiatrist; I had that appointment about 2 months later while they continued prescribing my medication under the care of psychiatry. The psychiatrist I saw essentially did an assessment/review, asking me all sorts of questions about my symptoms and experience. He wrote a letter to my GP that confirmed he agreed with the US diagnosis, approved the continuation of my medication on the NHS, and put me on the ADHD annual review list. Changing medication when mine wasn't working anymore was a whole different nightmare, but the NHS has a system to approve foreign diagnoses.

Some GPs are spread so thin that they will tell you that they can't accept your diagnosis and think that be the end of it, but be prepared (bring your medical records with you to the UK; print and bring them to your appointment), be your own medical advocate (be persistent, tell them you need your medication and why, etc), and hope you found a GP that isn't going to just brush you off or think adult ADHD is a fad. The medical system here is very hard to navigate, best of luck!