Is it permissible to complete a computer course that was not finished, at a time when the amount allocated for it has been disbursed, after moving to another government department?

Muslims are bound by their conditions. Therefore, the conditions set by the administration responsible for granting these funds to its employees must be considered and acted upon. If one of its conditions is that the course is exclusively for its employees and no one else, then the amount must be returned to the previous administration. But if that was not a condition, and it only stipulated attendance of the course, then there is no objection to attending it while you are in your new administration.