Is the questioner considered negligent and liable for anything for forgetting to convert 300,0 Syrian Pounds to dollars in a timely manner, which led to their being exchanged at a higher rate later?

A trustee is not liable unless there is transgression or negligence. Delaying the disbursement of money for a day is not considered negligence, as the trustee may not be able to initiate the process on the same day due due to circumstances that necessitate it. If the delay is due to excessive work or forgetfulness, there is no negligence or dereliction on his part, because one who forgets is excused. Therefore, you are not required to compensate your principal for the exchange rate difference.