Is it permissible for a paternal female cousin to correspond with her maternal male cousin who is imprisoned, and who considers her as a sister or daughter, with his wife reading the messages?

If the correspondence between a woman and her male relative is limited to asking questions and inquiring about well-being without suspicion, then there is no harm in it. This is because correspondence between the two genders is not absolutely forbidden except when there is suspicion or fear of fitna (temptation/strife). However, if it is for a need and fitna is secure, then it is permissible, especially between relatives.