Ketten spells the name as 'La Prospérine'. Dingee has the same spelling in its catalogues where the rose is described. 'La Proserpine' is a typo in the price list of 1910, which was then carried forward in the next issues. We add this spelling as a "hidden name", to enable search, but not as a synonym. Vick's 1901 'Proserpine' seems to be a tulip.
Right, that there was a 'Proserpine' tulip around; but 1901 Vick's 'La Proserpine' is definitely a rose, included on p. 95 under "Monthly Roses" with the likes of 'Hermosa' and 'Maman Cochet'.