student visa to skilled worker visa

I’m on a UK Student visa. I submitted my dissertation on 4 Aug and final presentation on 12 Aug, but my CAS says my course ends 30 Sept. My job starts 22 Sept, so my employer says the uni needs to notify UKVI of an earlier completion date.
Student Services are checking with my faculty, but staff are on leave. I’ve heard from others that UKVI was only updated after mark ratification in Oct, but I’m hoping it can be done sooner with a “completion of studies” letter.
Has anyone had their uni update UKVI before results are ratified? And would a letter alone work for the Skilled Worker switch?

Hi, my module directors wrote me a letter stating i have finished my course and awaiting results. however, my employer has not yet updated me whether that is enough to start my application. But i am applying for skilled worker visa. From what i know for graduate visa, thats after results are ratified and then only the uni sends you an updated number to apply for psw