Who reviews the postdoc file applications? (UK) I was informally invited to apply for a postdoc position at a university in the UK. The professor will be the PI of that project and said I can use the resume and the covering letter I had once for a postdoc. The problem is that the advertised position asks for certain skills that I didn't  highlight in the cover letter. So, I'm not sure if I should use trust the PI and use the original documents or I need to customize the files a bit more. Is the PI is the only person who reads the application documents? Or the files get analyzed first by the HR team and then they're sent to the PI?
Similarly to the answer of @YemonChoi above, the way recruitment is supposed to work at the place I have experience (n=2, higher than @Yemon, but not massively) is that HR passes the documents, mostly without reading them, to a recruitment pannel chaired by the PI who holds the grant.
The panel independently score the applicants on a predetermined scoring scheme matched the person specification drawn up for the position (and normally advertised with it) and the applicants with the highest scores are invited to interview. For any internal redeployment or disabled candidates that are not invited to interview, there most be an explicit reason why not.
Interviews are conducted using predetermined questions/activities and the panel score the interviewees independently. After the interviews, the panel confer, but ideally, the best performing candidate is offered the job first.
Thats the theory.
In practice, the PI generally decides who they want to interview, and checks that the rest of the panel agrees.
At interview, most panel members don't bother to score on the predetermined criteria. After the interview, they have a conversation, but in the end the PI makes the decision. Scores are then created to justify the decision made.
What this means for the OP is that if the PI wants you, the rest of the panel will not get much say. That said, it probably can't hurt to make some optimizations to your materials, unless that will be very time consuming and you worry about a soft or hard deadline, or creating a poor impression to the PI for being slow.