Is the amount allocated for gasoline allowance, which the manager pays to the accountant and is recorded under a different item to avoid inquiries from the company's head office and charged to the project, considered permissible or forbidden (halal or haram)?

Company funds are sacrosanct, and it is not permissible for you to take petrol allowance for your private car, which you sometimes use for work, unless authorized by a person delegated by the company owners or an official from the entity. If your manager, who is not authorized, orders this, then both of you are sinning, because the manager is disposing of another's property without a rightful claim, and this is considered treachery. In this case, you are voluntarily offering the use of your car, and you should inform the relevant authority to compensate you legitimately.