The FAA link shows the aircraft to be a 1944 V-77, which was derived from the Stinson SR-10, not from the earlier SR-9 Stinson series. The current FAA registration shows it as a Stinson. However, in 1940 Vultee purchased Stinson, so a 1944 V-77 should be of Vultee manufacture.
Re-registrations by subsequent owners of an aircraft (sometimes with a lapse) may result in such errors, and the FAA usually takes what the new owner provides for nomenclature, etc. Changes to correct such errors cost money and require documentation and thus registration errors errors usually prevail. In a similar situation in inquiring to correct an error, the FAA asked an owner friend of mine "Do you really want to go there?"
If you want to build one of the SR-9 series models, the V-77 would not be an entirely correct or appropriate reference.
You might wish to read my Stinson Reliant article on this site for further history and Stinson Reliant model differences. I share your interest in the SR-9; I built a model of one about 1943-44 from a commercial kit. I also have some SR-9 photographs on this site.