What is the ruling of Islam concerning someone who amassed a large amount of wealth from an illegitimate source, and is unable to determine its exact amount or its rightful owners due to its vastness and the passage of time, and how should they dispose of the profit generated from this original wealth?

The usurper is only required to return what he usurped because the usurper's hand is a hand of guarantee. This applies if the increase in the usurped property is in kind. However, if the increase is due to processing, such as transforming raw gold into jewelry or grinding wheat, the usurper is not entitled to any payment for that.