If you have the engine with the oil cooler, I would install the oil cooler.
With your donor engine out, I would recommend changing the gasket in between the engine and the oil filter housing. I sure wish I had.....

__________________
Jimmy L.
'05 Acura TL 6MT
2001 ML430 My Spare

Gone:
'95 E300 188K "Batmobile" Texas Unfriendly Black
'85 300TD 235K "The Wagon" Texas Friendly White
'80 240D 154K "China" Scar engine installed
'81 300TD 240K "Smash"
'80 240D 230K "The Squash"
'81 240D 293K"Scar" Rear ended harder than Elton John