Your Navy Luger is what is called the 1914 variation Navy. About 7900 with the year 1916 on the chamber were delivered to the 'Kriegsmarine'. Only few survived the war. And the treaty of Versailles after the war, where barrels longer than 4" were banned, took care of again many of the survivors. A lot of barrels where then shortened from 6" to 4".
What strucks me, is that you state a serial number of 639. I suppose that this is the # you can find on the frame, under the barrel, and also on the barrel itself. In your case it would mean that the serial number of the weapon matches the serial number given by the First Sea Batallion.
In Jan Still's 'Imperial Lugers' on page 195 there is only one more Luger reported with this unit marking: I.B.S. 681. It is not clear is that Luger had also a matching Serial Number of its own... May be Jan could look to that.
You have a fine Navy. Keep to it!