Is it possible to repent from lying to the professor with false accusations and fabricating evidence, with the ensuing measures that could lead to his dismissal, without apologizing to him to avoid increasing problems?

The repentance for the calumny that the questioner directed against his teacher requires him to promptly inform the administration that he lied in what he told them, so that the teacher is not dismissed from work. Regret alone is not enough; rather, an effort must be made to remove the harm inflicted upon the teacher.

The jurists have stated that whoever slanders a person, the slandered person has the right to have the slanderer retract his statement in front of those to whom he made it, if possible; otherwise, recourse is to Allah.

Furthermore, injustice to people carries great danger. Allah Almighty said: "And those who harm believing men and believing women for [something] other than what they have earned have certainly borne slander and a clear sin." And it has been authentically reported from the Prophet, peace and blessings be upon him: "And whoever says about a believer what is not in him, Allah will make him dwell in Radghat al-Khabal until he comes out of what he said." Radghat al-Khabal is the fluid extracted from the inhabitants of Hell.