Found another Wm. Schaefer & Son, Boston courtesy of Bro. Berck, with 'HAL'; H A Linder or H A Lewis maker stamp?

Without a maker's mark, all we can determine is that your tubes were sourced from Belgium, as were the vast majority of U.S. maker's, and most English maker's tubes. 'Rose pattern' Bernard II barrels were popular with the independent U.S. makers who used actions sourced from England and Lindner; William and James Donn of Canton and Peoria (William later in Chicago), George T. Abbey and Edwin Thomas Jr. in Chicago, and Martin F. Kennedy in St. Paul.
Maybe Dr Bill or Dr. Raimey will comment.