The SP depot is clearly visible just east of California Ave, about 200 yards north of Willow St. I went by there this afternoon, just as some city workers were in the process of leaving. I stopped and spoke with them briefly, and while they themselves weren't working on the depot, they know the crew that is. The roof is temporarily off while they complete reinforcing the structure inside. As you probably know, the building was cut into at least 2 parts for the move.
A photo courtesy of Google is here:
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www.google.com]
As an aside, the roadbed of the original LA Terminal/SPLA&SL/UP line into Long Beach is between California Ave and the depot. This section of the line was torn up not long after a bypass was completed in 1932 from what is now Douglas Junction to Terminal Island, running diagonally across North Long Beach. The original alignment has been obliterated in most places, but is clearly visible near the station, including a fill just north of it.
The roadbed and fill are visible here:
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www.google.com]
In the distance, it curves to the right, marked by a row of trees. The curve is more clearly seen in the overhead view.