Questions on an Early Inland

I just acquired an early Inland carbine in the 772,000 range. It has all the early features including high wood, push button safety, Type 1 band, correct Inland trigger housing and hammer, and flip sight. The barrel is dated 7-43.
I just took it apart. The left side of the receiver under the wood is stamped SG. The operating rod has a large S stamped on it. I know the SG designation was used by Saginaw, but wondered if it is correct for an Inland made carbine. I am also wondering about the S on the operating rod.

correct sg sub range, i have one too

SG made the receiver and sold it to Inland.

Is the 'large S' on the inside or the outside of the box section of the operating slide? It should have PI on the inside bottom and I believe a large letter (like an 'S') on the outside bottom.