Marc_Laf - I am getting a lot of "how to migrate" questions and will work on getting something formally documented.
Honestly though, the answer to that question was designed to be very simple. Let's assume you are already running legacy LAPS and are targeting a local admin account called "LapsAdmin". Here's what the migration might look like:
1) Extend your AD schema with the new Windows LAPS attributes
2) Add a new local admin account to your managed devices (call it "LapsAdmin2")
3) Enable the new Windows LAPS policies to target LapsAdmin2.
4) Run Windows LAPS and legacy LAPS side-by-side for as long as needed to gain confidence in the solution (and also update IT worker\helpdesk procedures, monitoring software, etc). Note you will have two (2) separately managed local managed accounts that you may choose to use during this time.
5) Once happy, remove the legacy LAPS CSE from your managed devices.
6) Delete the original LapsAdmin account.
7) (Optionally), purge the now defunct legacy LAPS policy registry entries.