Here is a catalog ad from 1910 showing all the types of Gillette Pocket Edition sets and what looks to be a previously undocumented type of Autostrop. It is an A model but has a floral style handle like the Gillette Pocket Editions. Unless this is something different this razor was a one piece made for these sets. If we go in order of production this razor technically should be designated as an A2 and the Autostrop currently designated as an A2 as an A3 instead.
I have seen catalogue pages that included Combination Sets that seemed identical to the No. 00 that incorporated a GEM instead of a Single Ring or other Gillette. I want to say I also saw one with a Autostrop(Not Valet) too.
Here you go on the Auto-Strop Combination Set Even as late as the 1930's(These are English, being sold in Sydney)
that Autostrop razor you picked up on would be amazing to come across. i have never been aware of this razor before. thnx for posting