Are the power supplies cross compatible?

Hi, just recently, I bought a used PS3 with the YLOD to fix, jailbreak, ect. The console is a CECHB01 (All Black, 20GB, Backward Compatible, 4 USB ports, and a card reader) and it did not come with a power supply. I have all the nessisary experience to repair the console, but once I reflow it, I have no way to power it on and test it.

So my Question is this:

I have a normal working CECHK01 (Newer, not backward compatible)PS3 that has a working power supply (I don't remember the PSU's model number, but I do know that it has a black plastic shell), can I take that power supply out of the CECHK01, and put it in the CECHB01 just to test it out, and make sure it works, or do I have to use a power supply designed for the CECHB01 specifically? If so, what model power supply do I need to buy?