REF OIL PUMP.

Hi everyone, new to the forum so would like to say high. Looking for some advise with the oil pump. Is there any means of testing it ?To cut a long story short i picked up a 1984 A5 which has been standing for many years. It was put to one side with a hole in no 1 piston and left under a cover.Its pretty bad but i thought i would try to rescue it. The engine is out and top end stripped and sump off. My consern is the bottom end as i have a spare block and cylinder head.The sump was full of white sludgy oil as expected and a few bits of the blown piston.I also found this .For the life of me i can't work out where it has come from, nor can find anything broken off. So any ideas ? But to start with i would like to know if i can check the oil pump is working before rebuilding the engine.

Can you take another picture of this piece on my computer anyway its very blurry.

Richard