Geting offered a job 3 weeks before my PSW visa expires?

I was last employed 6 months ago then took a break to pursue a professional diploma (to add to my masters degree as I'm switching fields) Been searching for work since.

My PSW visa expires in 3 weeks and I've finally had an employer that's interested in sponsoring me.
(The employer already holds a sponsor license and the job would be at level NQF 6. Also I've maintained the £900 funds)

Still unsure about a few things though:

-Am I still exempt from the labour market test solely based on the fact that I am in the UK under Tier 1 PSW? I keep seeing conflicting information, namely that I need to have worked for the employer for at least 6 months in order to be exempt from it.

-I'm also assuming I need to start working for them right away in order to start my tier 2 application? I know it will take them a few days to generate a certificate of sponsorship.

-Anything else that could potentially cause issues at this stage? My biggest worry is the labour market test.

Thanks!

u are exempt from RLMT becasue u are on psw.
the 6 months rule was abolished nearly 2 years ago.
u dont need to be working for them to start the visa application. u can start work now, or when u get the visa, either way you will be fine.

I agree, you're exempt from the RLMT. Also as a PSW-switcher your employer can assign you an unrestricted CoS.

The important thing now is for the employer to assign the CoS, making sure that your job description corresponds to the SOC code they're going to use, and that the salary they offer is no less than the minimum stated in the code of practice. Do note that the SOC code of practice was updated at the beginning of April, so make sure that you are referring to the current one. Also the Tier 2 Guidance was updated at the same time, along with the application form. The main difference as far as I can see is that now you can apply for five years leave upfront, rather than getting three years, and then extending. It costs more money though.