Is the money left by the plaintiff with the gold merchant considered unlawful, even though the plaintiff has no proof of the accuracy of the accounts?

A fatwa is not beneficial in matters of disputes and contentions; these are resolved by the Sharia judiciary. If the owner of the capital and the Mudarib (investing partner) disagree on the amount of the capital, and neither has proof, then the statement of the Mudarib is to be accepted, because he is an أمين (trustworthy).