If I borrowed money or was given a gift, is it obligatory to investigate the source of the money, and is it permissible to accept it if it is known to be unlawful?

The basic principle concerning the wealth of Muslims is permissibility. Therefore, as long as it is not proven or highly probable that a person's earnings are from illicit sources, there is no harm in borrowing from them or accepting their gift. Inquiring about the source of their wealth when its apparent state is sound is considered an excessive formality.