A HElizabeth

Hello, In August of this year, my partner successfully applied for an unmarried partner visa permitting him the right to work and live in the UK (he's a German native). Since then he's been applying for work but has had no luck, so we're looking into him working fully remotely for a German employer and living in the UK. We'd like to move into a London apartment together in the new year. I understand from the posts above he should: A) Declare his German employment income in a Self Assessment tax return each year. B) Contact the German tax authorities to let them know he will be permanently leaving Germany and find out how he ensures that his employment income is no longer taxed in Germany. Will both of these tasks need to be completed before he can move to the UK? And is there anything further that needs to be done? Thanks in advance!