No, the SIMs are interchangeable on the 5c, 5s, 6 and 6+. His phone number will travel with the SIM as will his girlfriend's. However, he will have to add the new phone to the account and pay the activation fee. That will require getting a new SIM from Sprint if he wants to use both phones on the same account but on different SIMs. If he doesn't get another SIM then he can shuttle the same SIM back and forth between the two phones but it will mean only one phone is active at a time.
Some things to note
1. Sprint has changed their unlock policy. As of 2/19/2015 all iPhones that are paid off (in whatever manner) will be automatically domestically and internationally unlocked. The only exceptions are the iPhone 4, 4s and the iPhone 5.
2. The SIM free Sprint model iPhone is already unlocked domestically and internationally.