Is it considered a false testimony when some students write down the names of their absent colleagues at the university, with the university's knowledge and the supervising professor's approval, and what is its ruling and expiation if it is indeed so?

It is not permissible to write the name of an absent student on the list of attendees, for this is a false statement and forbidden deception, based on the words of Allah Almighty: "And shun false statement" [Al-Hajj: 30], and the saying of the Prophet, peace and blessings be upon him: "Beware, and false speech and false testimony," and "Whoever deceives us is not of us." Falsification is imitating another's handwriting, or any statement or action intended to make falsehood appear as truth, and it is forbidden and falls under the general meaning of "Whoever deceives us is not of us." The claim of approval from the administration or teachers does not make it permissible, and one must repent to Allah with remorse, cessation, and a firm resolve not to return to it.