Is it obligatory for the questioner to inform his father of his fear that his paternal uncles will demand the repayment of his father’s debts after his death, knowing that they benefited from the trade that relied on these debts?

There is no harm in informing the father that he should document his rights with his siblings through documents that clarify the true rights. This is to prevent future disputes between the partners or their children. Writing and documentation are legally required in matters of debt, as Allah the Almighty says: (O you who have believed, when you contract a debt for a specified term, write it down).