Is the salary received by a person over 65 who changed his birth certificate to a younger age in order to remain in his job considered unlawful (haram)?

It is not permissible to manipulate the birth date recorded on the certificate for the purpose of continuing to work, because this involves deception, falsehood, and trickery. One must adhere to the employer's conditions, such as age limits, and it is forbidden to deceive them; due to the Prophet's (PBUH) saying: "Muslims are bound by their conditions," and due to the general proofs prohibiting deception and falsehood.