All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad is His slave and Messenger.
The money that is obtained from Riba (interest and/or usury) is ill-gotten money and it should not be given in charity because Allaah is pure and He only accepts that which is pure. Rather, one should get rid of this money by spending it on the general interest of Muslims. Therefore, that man may give this money to the mosque fund which you mentioned in the question so that it can be spent for the benefit of the mosque or that it will be spent on the poor and destitute people. For more benefit, please refer to Fatwa 85198.
It is not permissible for whoever gained ill-gotten money to spend it on himself or to invest it even in a lawful business.
As regards the ruling of lawful money that one earns from ill-gotten money (taken unjustly from someone else), then the preponderant opinion of the scholars is that he deserves half of the profit and he should give the other half to the owner of the money which is taken from him unjustly. Moreover, if he gained this ill-gotten money from Riba or else and then he invested it and made profits from it, then it is an obligation on him to spend half of this profit along with the capital money on the general interests of the Muslims, like building hospitals, schools and on other fields where ill-gotten money should be spent.
Allaah Knows best.