What is the ruling on the oath: "By Allah, there is no god but He, my prayer becomes unlawful for me if I say such a thing about you," if the one who swore it forgot the truth and was sincere in his intention at the time of the oath, then remembered the truth later?

If one swears an oath concerning something they did not do, while having forgotten that they did it, their oath is considered a "laghw" (unintended/vain oath) by most scholars. It is obligatory to seek forgiveness (istighfar) and repent for the ill speech towards the brother, and to be keen on praising him in the same gatherings. It is also advised to try to appease him by being kind to him. If the atmosphere is clear, one can be frank with him and apologize; otherwise, it is better to conceal the matter from him.