Yes, for the most part. Firearm transfers should go through both FFLs because: 1.) For easy transaction and 2.) legal issues.
Most FFLs are knowledgeble about gun laws from different states. They'll clear up any problems to make a smooth transfer.
Trust me, I learned the hard way. A seller in IL, shipped a handgun straight to my FFL. My FFL didn't know what to do since it didn't have the proper paperwork. I ended up selling the gun to my LEO friend, because the FFL dealer didn't want to deal with a handgun that was dropped in his lap.