What is the ruling on disposing of a deceased woman's money through ongoing charity (sadaqah jariyah) to build a mosque without the knowledge of her heirs, and is this permissible in Islamic law?

The sister's obligation is not discharged by donating money to the mosque, but rather she must return it to the heirs, because ownership transferred to them after the death of the inheritor. If all the heirs permit it, then she is not obligated to anything, provided they are adult and of sound mind. Otherwise, the share of the minor or the one who is not of sound mind must be returned.