The initial approval is valid for 4 months. The embassy can extend this if the case is still being worked on. Have you scheduled the interview or taken any action on the case since approval? If so, the embassy probably extended the petition's validity for you. The only way to really know for sure is to contact the embassy.
If the petition did expire and you don't have the visa yet, then you will need to start the process over.
If you have the visa (and the visa is not expired), then the petition's expiration doesn't matter.
Why would he need to wait a year to travel anywhere? Once he enters on a K-1, he has 90 days to marry then needs to file for AOS. He can (and it is highly recommended to do so) also file for AP and EAD. ETA: 3-4 months. AP will let him travel abroad for short trips. The EAD will let him work. He doesn't need to wait for the actual green card approval for these activities...just AP/EAD.
