USA S.U.B body compatible with sterling S.U.B. neck?

Got an old 4 string MusicMan S.U.B (2004) with a cracked truss rod and found a Sterling S.U.B. at a pawn shop for a good enough deal. My plan is to take the neck off the sterling and put it on the Musicman body. I know the neck profile will be thinner, which I’m not wild about, but if the neck pocket is compatible, it’ll be an improvement over the broken neck. So my question is, will it fit?