Is it permissible for me to continue in my job as an architect in a contracting office where I have learned that the employer practices fraud in calculating quantities of materials with contractors, and is the salary I receive from this job lawful or unlawful?

Allah has forbidden lying and deception, and "whoever deceives us is not of us." Taking specific quantities and billing contractors as if they were less, or vice-versa, is considered deception and consuming people's wealth unjustly.

Your friend must repent. If he can identify those he deceived, he must return the difference to them. Otherwise, he should give it as charity on their behalf. If he later finds them, he should offer them the choice between approving the charity given on their behalf or receiving the payment directly.

As for you, if your friend repents, you may continue working with him. Otherwise, it is not permissible for you to remain, as it constitutes aiding in sin. The salary you received before you knew about the deception is lawful for you. However, after you became aware, it is not permissible if your friend does not stop deceiving.