Is the son obligated to return the money he borrowed from his deceased father with an increase, knowing that the money was from an Islamic bank, and that the father refused to reclaim the money during his lifetime, considering it as if it were in the bank?

In religion, it is obligatory to repay a debt with its equivalent without any increase, unless the borrower wishes to increase it as an act of generosity. The son is only obligated to repay the amount of the debt without any increase. The amount the son borrowed from his father is considered a loan, not an investment, so the son is only required to repay the equivalent of the debt.