OK, I think you are asking about the signatures on the PQR. The employer's representative signs the PQR indicating it is accepted as meeting the requirements of the governing document.
The signatures on the PQR indicating the laboratory tests were acceptable is typically a representative of the contractor, be they a CWI or not, they represent the contractor. I would hope the original test reports are archived and available for review should they be requested by the client's auditor.
I attached the original laboratory reports to the PQR. Everything appears as a PDF and all the documentation, i.e., the PQR and supporting documentation such as CMTRs and laboratory test reports are combined into one PDF. The PQR refers to the laboratory report numbers and list who from the laboratory signed the laboratory test reports which can be cross referenced with the copy of the laboratory test report. Some of my PQRs with supporting documentation may be several pages long with all the supporting documentations.
Al