Is it obligatory to inquire about the source of money before trading with it if there is doubt about its source?

There is no obligation to investigate the source of the sister's money, for the fundamental principle regarding a Muslim's wealth is permissibility. Dealing with it is permissible unless it becomes known that the majority of her money is unlawful. Therefore, there is no harm in dealing with the sister, sharing in her money, and investing it in permissible ventures.