Is it permissible for a captive to smuggle out sperm for an embryo transfer to his wife, with whom he has a marriage contract, knowing that she is still a virgin?

Artificial insemination is impermissible except out of necessity or need. What is mentioned in the question does not fall under the category of necessity for performing this procedure, as the utmost concern is merely the fear of not being able to conceive in the future. Meanwhile, necessity or need is only realized when there is certainty of inability to conceive.