Is the salary increase obtained through forging a job offer and defrauding the company unlawful (haram), and what is its expiation?

Lying and deception are impermissible, especially in commutative contracts. The questioner must repent.

He must inform his company's management of the truth of the matter. If they approve of the increase, there is no blame upon him. If they do not approve, and the increase was due to his lying and deception, then they have the right to annul the contract and demand from him whatever exceeded the market rate for the previous period.

Ibn Muflih mentioned in "Al-Mubdiʿ" that the ruling on ijarah (leasing/hiring) is like that on bayʿ (selling). If the contract is annulled during its term, he is liable for the pro-rated market rate, not the stipulated amount. Sheikh Taqi al-Din mentioned that if the lessee defrauds the lessor and deceives him into leasing it for less than its value, then the lessor is entitled to the market rate.