A customer brought in a Lightweight Milestone (high-end German wheel manufacturer) for service.

It's a clincher setup, by the way.
The job itself was straightforward — they wanted me to swap out the DT star ratchet freebody from Shimano 11-speed to Campagnolo.
With DT freebodies, you have to replace the right endnut that comes with it as a set.
Since those dimensions differ between specifications, the wheel center will inevitably shift when you make the swap.
If the wheel was centered with a Shimano 11-speed freebody, it will definitely go out of center when you switch to a Campagnolo freebody.
Similar designs like the Mavic Cosmic Carbone Ultimate can be re-centered on the non-freeside by adjusting nipples,
and Reynolds RZR uses thin spacers on the left endnut — you adjust the number of spacers to dial in center.
With Lightweight... there's not much you can do about it,
but first I checked the center with the Shimano 11-speed freebody still installed.

When I held the gauge against the freeside,

↑there was this much gap on the non-freeside.

Next, after swapping to the Campagnolo freebody,
when I held the gauge against the non-freeside,

↑there was this much gap on the freeside.
I positioned the gauge so the gap shows on the hub side to make the offset more visible.

↑To sum it up, it works like this.
The Shimano 11-speed freebody plus right endnut assembly is longer in overall dimension,
so from the wheel center's perspective, the rim shifts toward the freeside when going from Shimano 11-speed to Campagnolo,
and shifts toward the non-freeside when going the other way.
In reality, it's the "wheel center" in the diagram that shifts due to the endnut dimension difference,
and the absolute positional relationship between hub body and rim stays fixed,
but I drew it this way because I wanted to focus on the apparent movement of the rim.
The problem with Lightweight is that this time, it just happened that Campagnolo had less center offset
(as shown in the diagram), but there's considerable unit-to-unit variation.
For example, some wheels center perfectly on Shimano 11-speed and shift significantly toward the freeside with Campagnolo.
When dimensions happen to line up favorably at some point, you can actually aim for perfect centering — and that's what happened this time.
I actually took detailed photos, but I'm not posting them here.
Come to think of it, I did something similar with an Autobahn before (here).
That was going from Shimano 10-speed to 11-speed though.

It's a clincher setup, by the way.
The job itself was straightforward — they wanted me to swap out the DT star ratchet freebody from Shimano 11-speed to Campagnolo.
With DT freebodies, you have to replace the right endnut that comes with it as a set.
Since those dimensions differ between specifications, the wheel center will inevitably shift when you make the swap.
If the wheel was centered with a Shimano 11-speed freebody, it will definitely go out of center when you switch to a Campagnolo freebody.
Similar designs like the Mavic Cosmic Carbone Ultimate can be re-centered on the non-freeside by adjusting nipples,
and Reynolds RZR uses thin spacers on the left endnut — you adjust the number of spacers to dial in center.
With Lightweight... there's not much you can do about it,
but first I checked the center with the Shimano 11-speed freebody still installed.

When I held the gauge against the freeside,

↑there was this much gap on the non-freeside.

Next, after swapping to the Campagnolo freebody,
when I held the gauge against the non-freeside,

↑there was this much gap on the freeside.
I positioned the gauge so the gap shows on the hub side to make the offset more visible.

↑To sum it up, it works like this.
The Shimano 11-speed freebody plus right endnut assembly is longer in overall dimension,
so from the wheel center's perspective, the rim shifts toward the freeside when going from Shimano 11-speed to Campagnolo,
and shifts toward the non-freeside when going the other way.
In reality, it's the "wheel center" in the diagram that shifts due to the endnut dimension difference,
and the absolute positional relationship between hub body and rim stays fixed,
but I drew it this way because I wanted to focus on the apparent movement of the rim.
The problem with Lightweight is that this time, it just happened that Campagnolo had less center offset
(as shown in the diagram), but there's considerable unit-to-unit variation.
For example, some wheels center perfectly on Shimano 11-speed and shift significantly toward the freeside with Campagnolo.
When dimensions happen to line up favorably at some point, you can actually aim for perfect centering — and that's what happened this time.
I actually took detailed photos, but I'm not posting them here.
Come to think of it, I did something similar with an Autobahn before (here).
That was going from Shimano 10-speed to 11-speed though.