Powershell : migrate Exchange 2010 on-prem mailbox to Office 365 and more.....

Hi Mates,
here below a script that I've used to migrate some users to Office 365.
The script contains a lot of comments that should explain sufficiently what it does during the several steps.
Consider that I had a bunch of needs : change some group membership , change the quota, apply email address policy and so on.
For sure it is amendable but at least it's a decent starting point.