Normally we might relegate these to the giant group of pieces simply marked "Sterling Handle". A vaiety of designs are so marked. I have seen one set with Frank Whiting's cat whiskers mark, and this fork has the latter version of the Pythagorean symbol or tri-box Rogers Lunt & Bowlen mark (just the B, not the B Co.). [I would take it that this other version remained in use after 1935.] The HH seems to be most likened to the Early American pattern of their flatware designs. As usual, the wood is marked "FRANCE", in this case about 1/3 of the way up. (Crosscut/diagonal saw or file marks remain visible between the tines.) Are we possibly looking at a specialty manufacturer importing the wood to couple with handles they acquire, or a single supplier sending wood parts to the silvermaking firms themselves? Yes, the photos suck, but I checked the marks with a loupe.
I should note that the wood pieces seem standardized and thus do not always make a perfect transitional fit with the sterling..this one is pretty good. I would expect that the silvermakers would be more demanding of the fit if they were finishing these items themselves. There is also some counterbalancing weighting within the hollow metal that seems greater than the light wood could explain, so filling material appears likely even though not noted in the marks by the silvermakers.