Is it permissible for a student who obtained a general secondary school certificate through bribery to continue in his job, knowing that this certificate is his source of livelihood, and that he is at a good academic level and is about to become a university professor?

There is no harm in continuing the work if the skills qualify for it. If the bribe was paid to obtain something that was not rightfully due, then it is a sin and one must repent from it, but it does not prevent continuing in the work. However, if the bribe was paid only to obtain one's right, then there is no sin upon the one who paid it, and the sin is upon the one who received the bribe. This is permissible according to the majority of scholars.