Is it permissible for me to settle the 3800 EGP that was lost by my colleague at work – which he had taken to perform my duties during my leave and was stolen from him in his office – in a way that the employer bears it without his knowledge, knowing that if he knew, he would refuse to bear the amount?

If the employer assigned your colleague to accounting, then he is entrusted with the money and is not liable unless he neglects or transgresses. If the theft occurred due to his negligence in safeguarding it, then he is liable for the money. In this case, you are not permitted to settle the amount for the employer to bear. However, if the theft occurred without negligence, he is not liable, and you are permitted to prevent injustice from him by settling the amount. It should be noted that if your colleague undertook accounting without knowledge and caused the loss of money, then he is liable because he is a transgressor due to his ignorance.