The poster is the same design as the cover, and it is signed HBP.
Different institutions have attributed this to different designers. The New York Public Library's collection of posters has the designer listed as H.B. Pennell. The same poster held in the Huntington Library is credited to Maurice Brazil Pendergast, which is probably due to the monogram being confused for MBP rather than HBP.
An article in an issue of "Book News" credits a "Mr. Henry C. Pennell" for the design of the cover and title page of this book. Assuming that the middle initial "C" was an error and should have been "Henry B. Pennell".