It could be a cigarette holder but without dimensions it's hard to say. Frankau started BBB pipes which stood for Blumfeld's Best Briar. Louis Blumfeld worked for Adolphus as a very young man and ran the company after Mr. Frankau's death in 1856. The company was later acquired by Oppenheimer and "BBB" came to mean Britain's Best Briar.
In regards to smoking cigarettes which could be it seems a little short even for a male smoker. Looks like it might be for a smaller ring cigar? Nice craftsmanship.