Is it a sin for an employee to use his colleague's damaged gloves without his knowledge, and then replace them with a different type, knowing their source and that he approved taking them?

The questioner is not liable for what was mentioned, as he sought permission from its owner and knew that the latter had no objection to his use and disposal of the gloves. This is because such items are typically discarded by people due to their disinterest in them, and he has a greater right to them. He has dispelled doubt with certainty, so there is no liability or sin upon him.