What is the ruling on money earned from working after buying a university degree and enrolling in distance learning in the same specialization? And does studying the same specialization later on absolve one of the sin of buying the degree? And what must one do to expiate for this act?

Obtaining a certificate through cheating and forgery is forbidden and impermissible, based on the Almighty's saying: "So avoid the word of falsehood," and the Prophet's (peace be upon him) saying: "He who cheats is not of us." You must seek forgiveness and repent from it. Your enrollment in studies to obtain a valid certificate is a good thing, but it does not permit the use of a forged certificate. What you earn from your work is permissible if you master it and perform it as required, because it is in exchange for the work, not the certificate. This is what Sheikh Ibn Baz ruled.