Living in the Soo and being into postal history, I'm fascinated by the idea that at a time there were well over 10 post offices in the area that now comprises Sault Ste. Marie. Driving around town, you'd never know it. I think many were based out of small businesses or people's homes.
Here's a postcard stamped at the 'Sault Ste. Marie West' office:

To find out where this post office was at the time it was stamped (because it moved around), I first checked the Archives Canada site and found the postmaster at the time to be:

Next, I checked the archived 1907 Sault Ste. Marie city directory and came up with:

To the best of my knowledge, the shorthand in the directory translates to: Mark Cahill, working in real estate and as the postmaster of Sault Ste. Marie West in a building on the south side of Albert St., first building to the east of Gore Street. He lived at 77 Gore Street, about three blocks away. The reason I had to look up Mark Cahill's information is because the only post office listed under 'post offices' in the city directories of the time is the main office that now serves as the city's museum.
In any case, the 1910 directory actually provides street numbers for this spot:

The 1911 city directory shows the same property as being vacant, corresponding with the above noted date that Mark Cahill vacated the role of postmaster (also suggesting that the city directory for any given year must have come out near the very end of the year to be so accurate, given that Mark Cahill was apparently working as postmaster until November 2, 1911):

In 1912, it appears that a shoe seller and a shoe maker moved into the building(s?) that once housed the SSM West post office and Mark Cahill's real estate business, with one unit remaining vacant:

Subsequent directories indicate that Mark Cahill actually moved back into 11 Albert St. to continue with his real estate business in 1913, yet vacates the building again in 1914 along with the shoemaker and a company called 'Oxypathor Co.' that had set up shop in that same complex in 1913, leaving the complex completely vacant. In 1915, there is no longer any reference to 9-13 Albert St., indicating that perhaps the building(s?) were torn down or, if it was a multi-unit complex, the entire complex was renumbered to 15.
Either way, at some point it was torn down because here's a picture of that location today, just an empty parking lot:

The post office itself remained open until some time after 1966, operating out of various buildings on Gore Street. If I can find more SSM West postmarked materials (seemingly rare), I'll try to locate the offices where they were stamped. Next, I'm going to try to determine the location of the Steelton office (Steelton amalgamated with the Soo in 1918).