What is the ruling regarding a husband who married his paternal cousin, then left her for a year, whereupon he returned to find her pregnant and she gave birth five and a half months after his return, and she confessed that she had been raped, so he divorced her and married another? Was what he did correct?

Your friend's concealment of his wife's act would have been permissible if the matter was merely about adultery. However, since she is pregnant and the child is not his, he was obligated to perform li'an (oath of condemnation) to disavow the pregnancy. If he did not do so, the child is now attributed to him and cannot be disavowed, based on the Prophet's (PBUH) saying: "The child is for the firash (marriage bed), and for the fornicator is the stone [i.e., deprivation/rejection]," and due to the lapse of the condition of promptness in performing li'an. Furthermore, the wife's admission of rape does not negate lineage. We advise your friend not to neglect his two children and to fulfill his duties towards them, including financial support and upbringing.