What is the ruling regarding the remaining amount of money invested with someone, knowing that he has forgotten its value and so have I, and he says it is 1500 while I believe it is 800?

It is not permissible for a Muslim to delay the rights of others when he is able to fulfill them, as that is an act of injustice. In this matter, the statement of the mudarib (investing partner) is acted upon, and his acknowledgment is taken. If he acknowledges a certain amount, then forgets, and then acknowledges a larger amount, it is best to remind him of what he said first, and to act upon whatever acknowledgment becomes settled.