Brake cylinder compatibility (rear brakes...)

[zektiv]

So I've got this 03 XB9R that I'm hammering away at, and it looks like the rear brake is frozen. At least, the foot pedal is, because the rear wheel turns freely so clearly the brake isn't applied. I wrestled it off the bike and applied my sweetest kung fu moves on it to disassemble it, and the cylinder inside is rusted to spit or something, because it's (as they say in some neighborhoods) on lock. Will not move. I've dumped some PB blaster in there, maybe it'll move, maybe it won't, but at this point I'm thinking my best best is going to be to go ahead and grab myself a new brake cylinder/pump for the rear. After this lengthy preamble, here's my question:

Is the 1125 rear brake cylinder the same as the one on the XB? Sure looks the same. I see a few on FleaBay that are new (or like new) and a decent price. I'm just looking for it to bolt right up and be ready to roll. Or do I have to get the specific brake for the XB?

Any and all advice is much appreciated!!!

[Cosworth]

they have different part numbers but that doesn't necessarily mean they are different. I think I have both at home, I can check when I get home this afternoon and let you know what I see if nobody else chimes in.
1125 Rear master H0205.1AM
XB rear master H0205.1AA

I used a Ducati rear master and caliper when I did the hidden caliper mod. So I should have the stock XB one in my parts bin.