What is the ruling on dealing with a person who claims to be a creditor of my deceased brother for an amount of 1600 pounds, and possesses no proof of this debt?

The burden of proof is on the claimant, and the oath is on the one who denies. Therefore, this man must prove his claim with evidence to receive his right; otherwise, you are not obliged to give him anything. However, if you are strongly inclined to believe he is truthful, then give him what he asks for to clear your brother's conscience. Paying your brother's debt is (done) from his estate, and if he did not leave anything, you are not obliged to pay it, even though it is desirable and among the best acts of drawing closer to Allah.