One or more "
Conjugal visit" might be the better way to do this (assuming such visits are permitted in the prison at issue).
Not only permitted in the prison, but for the inmate. Conjugal visits are generally allowed only for those convicted of more minor crimes, usually not involving violence. They would be in a minimum security prison.
So, I would agree that the first place to ask is the prison's warden.
As others have noted, the method of transport will have to be discussed with a sperm bank or fertility specialist. On the other hand I will disagree somewhat with Alty. I may just be as simple as a turkey baster assuming the semen was transported properly. However, the odds of conception are not that great that way. But it is possible for that to work. The better option would be to have the semen shipped to a clinic that can then impregnate.