Carb Rebuild Kit For Craftsman 536.772320 Edger?

Hello. Does anyone know what the part number is for the carburetor rebuild kit for a 2002 Craftsman 536.772320 edger? It has a 3.5 hp 4 cycle B&S engine. Carburetor is unique, the fuel bowl is built in to the fuel tank which mounts directly below the carburetor assembly. Thanks!

First off that is not a special carb. They have been building them that way for decades. Second. Can not get any info on the engine without the model number of the engine.

The only numbers that exist are on the frame. Cannot identify any numbers on the engine.

I believe I found a new gasket, diaphragm, and primer bulb on ebay for the B&S "Pulsa Prime" engine. My research pointed in that direction, and the gasket and diaphragm look to be correct. Have not received them yet, though.

Seems to be a fuel starvation issue after running for a bit. Starts fine and easily and will run great but eventually will cycle through like it is going to die, low RPM, etc. Sometimes it will die out but other times it just keeps running poorly. Hoping the diaphragm fixes it, after all, I cleaned it with brake cleaner when I cleaned the carb. Thinking that the old 15 year old diaphragm didn't like such a harsh solvent.