PGR was a derailleur brand founded by Duilio Accorsi in Bologna, Italy. It has been suggested that PGR stands for 'Perfezione Gradualmente Raggiunta' which may translate as 'Perfection Gradually Achieved'. This seems a little strange as a brand name, but, if real, it is an interesting, distant, antecedant of Dave Brailsford's concept of 'marginal gains'.
I am aware of two PGR derailleur models, the single pulley PGR 2 and the double pulley PGR 3. It seems logical that there should also be a PGR 1 of some sort - but I have yet to see any evidence of it. My PGR 3 has 'Brevetti Accorsi' stamped on the head of its b-pivot bolt, indicating that there should be a patent trail hidden somewhere in the impenetrable vaults of the Italian Patent Office. The outer pulley cage plate of the PGR 3 is also stamped 'Camp. Italiano Dillet. 1948'. This may indicate that it was used by the Italian Amateur Champion in 1948 - a title that appears to be held by one Alfo Ferrari. This provides some evidence that the PGR brand was active in the 1940s.
Various Italian websites suggest that, before founding his own company, Duilio Accorsi worked as an engineer for Sabiem, a lift manufacturing company that is/was a close neighboour of the Ducati motorcycle factory. They also suggest that PGR may have gone on to produce parallelogram derailleurs, perhaps in the 1950s, and, perhaps, cheekily infringing Campagnolo's patents.
Finally there is a present day cycle and motorcycle business called 'Accorsi Luigi Eredi Vend. Rip. Cicli E Motocicli' in Cento, a town about 30km from Bologna. I doubt that this has anything to do with Duilio Accorsi, but you never know.