Am I obligated to pay a debt claimed by someone against my deceased son, knowing that my son denied it before his death, and his friend confirmed the falsity of the claim? And will I be held accountable for not paying this debt despite my doubt regarding its validity?

A debt claim against the deceased is not admissible unless there is evidence or an acknowledgment from their heirs. The claimant must provide evidence along with an oath. If they fail to provide evidence, your son is not obligated to pay anything. The Prophet, peace and blessings be upon him, said: "Were people to be given according to their claims, some would claim the blood and wealth of others. But the oath is incumbent upon the defendant." Paying the disputed debt to the claimant is more cautious and absolves your son's responsibility. If it is not rightfully theirs, it will be a treasure for you and your son on the Day of Resurrection.