Does divorce take place if the wife continues her studies after her husband gave her the choice between him and her studies, and she chose him, and then he later permitted her to complete her studies?

A husband's statement to his wife, "It's either me or the university," has three scenarios:

The first scenario: He intends to give her a choice between completing her university studies and divorce. If the wife chooses her husband (as in your case), the preponderant opinion is that no divorce occurs. This is the view of the majority of the Companions and scholars, who cite the statement of Aisha, may Allah be pleased with her: "The Messenger of Allah (peace be upon him) gave us a choice, and we chose him, so he did not consider it a divorce." Others held that it is a revocable divorce. However, if the wife chooses herself, there is a difference of opinion as to whether it is a revocable divorce, an irrevocable divorce, or three divorces. The jurists of the Zahiri school and some Companions held that giving a choice does not result in divorce at all.

The second scenario: He merely intends to threaten her with divorce if she chooses to study. This has no consequence, because a threat of divorce does not bring about a divorce.

The third scenario: He does not intend divorce or a threat of it, but rather intends to give her a choice between completing her studies and his affection and love. This has no consequence.

In summary: As long as your wife has chosen you, nothing results from that according to the preponderant opinion among scholars. There is no harm in allowing her to complete her studies if it is free from legal prohibitions.