I thought at first that this Eberhard Faber cap/extender might be a Protoclip without the clip, but it isn’t. It turns out that the design is similar to several other caps though, such as this one found in a late-1800s A.W. Faber catalog:
The design looks so similar to me that it makes me wonder to what extent the fledgling Eberhard Faber Co. may have appropriated designs from A.W. Faber after their falling out in the 1850s.
As early as 1900 there was a Mongol version of this cap, complete with a gilt band:
And here are some slightly different models, ca. 1905:
There is a 1916 patent assigned to Lothar Faber for a similar cap, but with a pocket clip as well:
The following are examples that look just as similar though they are from other companies. First is a Dixon cap from 1917 and second is an offering from the Eugene Dietzgen Drafting Company from 1928:
It’s called the Bijou Pocket Pencil 1585. The stamp on the original pencil is very faint which is why I didn’t include it in a photo. There is also a metal cap that came with it which matches this description found in Northeast Stationer and Printer Magazine from 1901:
Despite what appears to be threading the cap doesn’t screw on, but it’s still a snug fit: