Hi @alex132,
You can start working full-time from the end of your course (or the 1st year of your PhD) and there are no restrictions on you working full-time on your current tier 4 (student) visa until you switch it to Tier 2 (work) visa before it expires.
You can send the following links to your employer:
* Home Office Guidance on Tier 4 student full time work - section 272 , page 6 - Also available in the following link: https://assets.publishing.service.gov.u ... r_2019.pdf)
* Your Right to work on government portal:
Link: https://www.gov.uk/view-right-to-work
Share code: provided on the website
Date of birth : yours
Good luck !