I have not heard of a law department that sent a paralegal to work in a law firm for a period so that the paralegal picks up enough to carry on back in the department. We might call that practice a “reverse secondment.”
An investment by the law department, an acceptance by the law firm that training the paralegal might lessen their fees but strengthen their ties, and a general increase in flexibility and capability in the law department, all make such an idea worth considering.