I always fill the filter up before screwing it on as it saves putting a little oil through the little filler hole and also makes sure the oil pump and big ends get an immediate supply on the first start up.
Who changes the oil in the cooler? When you think about it there is always old oil trapped in the cooler, as the pipes are at the top. I've drained and re-filled it a couple of times but it's fiddly and messy, not very much oil in there either.
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