How was it delivered without a signature? If that was not authorized by your BF, then the shipper should be liable for it. If your BF gave his permission for it to be delivered without a signature, then it's on him, and he's likely SOL.
You could try monitoring local eBay and/or CL sales of "New, In box iPhones", especially if you have the serial number and IMEI number from Apple. If you find someone selling one matching the description of your BF's phone, ask for the numbers to make sure it's not locked. And then report to the police ASAP. After reporting your BF's phone as stolen, as mentioned above, of course...
C