"Oil is coming from the fuel pump."
" it begins to smoke - white "

Fuel pump may be bad OR head gasket may be blown. You can bypass, plug, the fuel pump using a temporary tank if necessary. Is the oil contaminated with gasoline?

Blown head gasket is common on this engine.

Walt Conner

I will check whether the oil is contaminated with gas after work this evening. You mentioned bypassing the fuel pump to isolate that as the problem. Is that as simple as running the fuel line around the pump straight to the carb?

" You mentioned bypassing the fuel pump to isolate that as the problem. Is that as simple as running the fuel line around the pump straight to the carb?"

Only if the tank is higher than the carb inlet so it will gravity feed.

Walt Conner

I have the same problem with briggs and sratton engine 31P777-0296-E1 on my sears craftsman lawn tractor. Oil is splashing from fuel pump area.

How do you make sure fuel pump is hooked correctly, which hose goes where?

Any U tube video, how to replace head gasket ( should that be the cause of above problem) on this engine?

There may be a number of how to you tube videos at that site.
Shouldn't be too hard to search them out.
Photo below shows the correct hose orientation for fuel pump.
INLET hose is from fuel tank/filter. OUTLET hose to carb. PULSE hose goes to valve cover, or to the crankcase or oil dipstick tube (depending on how the tractor OEM wanted it to be).
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