I don't know what the name of the manufacturer is, but do have the following Czech cases with the "R" marking:
9cm Mountain Howitzer, Vz.28 (90 x 78.5R) (1933) (different style of “R”)
10cm Howitzer, Vz.14/19 (100 x 183R) (1925) (same style of “R”)
15cm Heavy Field Howitzer (150 x 296R) (1930) (different style of “R”)
30.5cm Mortar, Vz.16 (305 x 382R) (1927) (same style of “R”)
In addition, I have a drawing of a 37 x 57R (Czech made Austro-Hungarian M.15 Infantry Gun (1926) round with the same “R” in the headstamp.
Based on these cases, it appears that the style of “R” on the 37.2mm case was used at least during the 1925 through 1927 period. I suspect that this case may be an experimental item due to the lack of a lot number.