Is it permissible to utilize free time at work to study Islamic sciences or listen to their lectures without the manager's knowledge, especially since the manager requests learning other things in preparation for an emergency that might occur to colleagues?

Working hours are the property of the employer, and it is not permissible to use them for anything other than the work's benefit, except with the permission of the authorized manager. One must be diligent in fulfilling the trust of work by utilizing their time for its interests, especially if the manager explicitly requests it. The pursuit of Islamic knowledge should be outside working hours, or after completing all work tasks and requirements.