You will require certain specialized tools and measuring equipment.
It assumes that the gearbox is in good condition, the preload of the taper roller bearings and position of the crown wheel is correct. You are using the same crown wheel.
The gearbox has been cleaned (I have machined alloy bungs to fit into the driveshaft seals to stop any ingress of water and foreign bodies)

The bolts have been removed that hold the two halves of the gearbox together along with the sealing bung, plastic disk and Hex tubular bolt ( I used a tool made from an old clutch driven plate to lock the first motion shaft so that the tubular bolt can be removed).
I have made a tool to push the shaft out of the bearing so that the gearbox can be split. A light tap may be required with a soft faced mallet to the diff' end to break the seal and disengage the locating dowels.

Gearbox split and diff' removed.

The bearings are removed, I have made a puller to do this so that no damage is caused to the bearings. Any shims need to be kept to the respective end and bearing.

A ground Parallel and depth micrometer is used to measure the distance from the crown wheel face to the bearing seating face ( I measure with and without the shim to double check myself) and the dimensions noted down.

The diff' is turned over, rested on a surface plate and dimension measured using a vernier height gauge from the crown wheel face to the opposing bearing seating face (and shim) and measurements recorded.

The crown wheel has been removed from the open diff' and fitted to the LSD.
The dimensions to the face where the bearings sit (including the shim) need to be identical to the original measurements. It is unlikely that the original shims will be suitable due to manufacturing tolerances between components (in this instance the overall dimension from one face to the other was 0.008 thousands of an inch different, this would have a significant effect on the bearing preload and relative position of the crown wheel). The thickness of the new shims is worked out by simple arithmetic from the original and new dimensions. New shims in various sizes are available from the dealers. The thickness of the original shim needs to be measured as it is not marked on them. (Both shims need to be determined)

The bearings are now fitted with the new shims, being careful not to damage the bearings by supporting the crown wheel off the bed of the press and only pressing on the inner race of the bearings and not the cages.

The LSD assembly is now fitted to the gearbox and the gearbox sealed.