Is it permissible to buy a house through the bank with an interest rate, knowing that the borrower has the financial capacity to pay rental installments?

Purchasing a house through an interest-based loan from a bank is forbidden in Islamic law. It is explicitly prohibited and not merely a matter of doubt. Several fatwas have been issued to this effect by scholars and Fiqh academies. Your friend can look for permissible alternatives for ownership, such as Murabaha (cost-plus financing) with deferred payment, or Istisna' (manufacturing contract) through institutions and companies that offer such transactions.