Jack Favell is Rebecca's first cousin, her childhood friend, and, it seems, her lover. (We know: ew.) Jack comes across as a crude kind of hustler, playboy type. He's low on cash, he's perpetually drunk, and he's often making inappropriate sexual comments.
Favell is the only person outside the players in the cover-up who suspects that Maxim killed Rebecca. His suspicion is even news to Mrs. Danvers, who assumed that Maxim's suffering after Rebecca's death was out of love and grief. Yet, Favell isn't really out for justice for Rebecca. He uses his suspicions to try to extort Maxim (get money from him) and ultimately doesn't seem to be grieving for Rebecca at all.