Görtz and Bryans covers aspects of all three eras, including the Reichswehr period when R=Reiter/Rider, but Imperial era such distinctions are more specific, Hussars, Dragoons, etc.. The "R" usually means an infantry regiment, bold for a line regiment, incursive a reserve IR.
This rifle appears to be a c-block, which would be a new high for Amberg, - currently the high does go into the c-block, but only marginally and even then it is a report. I do not suppose the owner stated the serial number? It would be useful to at east know how far into the c-block this goes, it looks like the serial could be a 6000 or 8000 c-block. A considerable jump over known production.