Is the amount disbursed to cover funeral expenses, when it exceeds the actual expenditure, the sole right of the person who paid the costs, or should the remaining amount be distributed among the heirs?

The default rule is that the expenses for preparing the deceased are taken from their estate, and these expenses take precedence over paying off their debts, executing their will, and distributing their inheritance. If an entity donates the funeral expenses (such as insurance companies), then whatever is spent from it on the funeral is considered part of the estate, and any surplus is divided among the heirs. If you paid the funeral expenses with the intention of recovering them from what the insurance company pays, then you are permitted to take what you paid. However, if you paid them as a donation, you are not allowed to retract your gift, and the money received from the insurance company is divided among the heirs, unless the heirs agree to give you what you spent and divide the remainder.