is the cobalt ss 4 door the same rear as the 2 door?

You could try a search over at the cobalt site Cobalt SS Network -

It looks to be the same for 2-door and 4-door, and although product fitment/application does not list that it fits HHR, Frenchy42 says that it does.

AXLE KIT. Rear Axle. SUSPENSION/REAR for 2009 Chevrolet Cobalt. #15232753

Yes, mechanically, they are the same car. Just as, mechanically, the HHR is identical to the Cobalt. Suspension, brakes, exhaust, even motors and trans are all the same across the lines, with the exeption of the ethanol motors not being put in the Cobalt, and the LSJ never being in the HHR.

Short of body/interior parts, if it fits a Cobalt, it fits the HHR. The only thing I've found so far that requires modification, is the exhaust that I mentioned before.

The part numbers are completely different, but that could be because one has a different size bolt hole or something.

All I know is that I installed a Cobalt rear axle on my HHR, and it went in with 0 issues.

You bought a 4 door SS , didn't you! Then we have confirmed a 4 door SS rear axle works!
Anybody use a rear axle from a 2 door Cobalt? That can confirm that fits an HHR?

The link that RJ posted says that the axle fits both 4 and 2 door Cobalts, so I guess that proves it?

Why not get an axle beam for an HHR SS?

To hard to find in a parts yard!