96 cold start runs dies runs great once warmed up

Ok so I bought this truck a few months ago. The previous owner changed the following
Gpr
Ipc i
Ipr
Uvch
Idm
Pcm
Cps
Oil pressure sensor
Lop
He could not get it to run correct after all this, I got a good deal I thought at the time Now it's haunting me on it's starting habits

So when it sits over nite " the hpop res is full" and you go to crank on it it will start and run long enough to run the oil out of the hpop then dies , check the res and it's empty. Fill it up and it will start and run Then the dummy gauge jumps up and shows oil psi. Now driving it all day it starts fine and runs fine it's just the first cold staRt of the day is a real pain



96 f-250 7.3 stock 4x4 a/t work truck

Try a Factory Ford oil filter.

It does have a Baldwin oil filter on it now