What is the ruling on a manager and some employees signing incorrect papers and data to obtain a quality certificate, with the auditor's knowledge and approval?

It is not permissible to sign papers with an incorrect date, nor to sign off on the completion of work that has not actually been completed, because this constitutes lying, deception, and fraud. This applies to both the company official and the auditor, as both are abusers and deceivers. The Messenger of Allah, may Allah’s prayers and peace be upon him, said: "Whoever cheats is not one of us," and he also said: "The two parties in a transaction have the option as long as they have not parted. If they are truthful and clarify, their transaction will be blessed. But if they lie and conceal, the blessing of their transaction will be erased."