You need to get one out of another 4.8. All of the differentials from E53 physically swap (you have to use the output shafts that go with the diff you want to use; they are all different) but each engine has a different diff ratio.

If you really wanted to use one from another engined e53 (say a 3.0 with 4.10 ratio) then you need to change BOTH differentials-front and back, because they are both the same ratio, and running mismatched dif ratios is...ill advised.

I don't know if 4.8s can suffer from stripped front driveshaft spline syndrome, but if they can, you might check that first before you give up on the diff.

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2001 E53 3.0 5pd