I used this Les - click for source - you will need two bottles as despite what manual says mine took 1.6 litres with car level on ramp.

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It's suitable for LSD diffs and contains a friction modifier. Been in for a few years now and it cured the clicking I was getting when maneovering on full lock. Likely better than adding pure friction modifier into existing dirty oil. Be aware there is an NS suffix variant for racing which doesn't contain the needed friction modifier.

I used my Draper hand operated gear oil pump from below. This avoids spill when filling from above and has a convenient hook on end of pipe for attachment to filler hole.