Is it permissible to establish a factory using funds from a bequest (one-third of the wealth bequeathed to the poor), such that its income serves as ongoing charity (Sadaqah Jariyah) for the poor?

The general principle for a will is that it should be executed as it is, and not altered unless it contradicts Islamic law, based on the Almighty's saying: "Then whoever alters it after he has heard it, the sin is only upon those who alter it. Indeed, Allah is Hearing and Knowing."

As for changing a will for something better, there is a difference of opinion:

Some scholars prohibited it due to the generality of the verse. Others permitted it because the purpose is to draw closer to Allah and benefit the legatee, and because the Prophet (peace be upon him) allowed changing a vow to something better.

The most preponderant view is that if the will is for a specific entity, it is not permissible to change it. However, if it is for an unspecific beneficiary (such as mosques or the poor), there is no harm in directing it towards what is better.