What is the wise and just course of action toward a person suspected of stealing money from his brother, taking into account the passage of time, the lack of conclusive evidence, and the need to maintain confidentiality and avoid creating discord among the brothers?

You may not accuse your uncle of theft, as you did not see him steal. He may have been counting money or intended to take it but did not. Testimony based on mere conjecture is not valid. You must advise the other uncle to safeguard his money in a way that does not cause problems or accuse anyone.