What is the ruling of Islamic law regarding a brother's refusal to repay a debt to his sister for fifteen years, and then, after this long period which caused harm to the lender, he wishes to repay only the principal amount of the debt?

Your brother is unjust for procrastinating in repaying the debt for a long time. However, you are not entitled to demand an increase from him as compensation for lost profit, because that is speculative. Resolutions of Islamic Fiqh Academies and Sharia Standards have stipulated the prohibition of stipulating financial compensation from a debtor who delays repayment.