Is it permissible for my father to work in a usurious bank, especially after his transfer to an administrative position, given the unavailability of Islamic banks in our country?

Working in a usurious bank is absolutely forbidden. The types of work within it vary in the degree of prohibition. Directly committing a forbidden act or strongly assisting and causing it increases the prohibition due to the general saying of Allah Almighty: "And do not cooperate in sin and aggression," and due to the saying of the Prophet, peace and blessings be upon him: "Allah has cursed the one who consumes Riba, the one who pays it, the one who writes it, and its two witnesses." Your father must repent and leave the job immediately, unless he is in a state of necessity, such that he cannot find another permissible job, in which case he is allowed to remain until he finds work.