OK I've found the solution, and it's stupid.
The person that could not validate the link was not eligible to that service (custom domain name) because she was not iCloud+...
Let me elaborate.
I would have thought that only one person (me, in that case) has to be iCloud+ in order to give to it's family the benefit of custom domain. It's true but, in order to do that, it is required to share iCloud+ subscription with its family before inviting them to join the custom domain.
In my case, I have iCloud+ (obviously), my girlfriend too, but not my mom. So during the migration everything was ok until she has to validate her email address.
So all was needed for me was to share the iCloud+ benefit to my family. Then everything worked.
I've manage to find a note in the Use Custom Email Domain with iCloud Mail - Apple Support page that says:
If you share iCloud+ with your Family Sharing group, you can share your
custom domain with your Family sharing group and allow them to create
personalized addresses.
In other words: if you don't share iCloud+ in your family, maybe because you don't want them to eat your precious (and costly) iCloud storage space, then you cannot share a custom domain with them. That service is directly tied with iCloud+ subscription.
That note is absent to the iCloud User Guide.
Here is what I would recommend to Apple :
- make it clear in all documentation that a iCloud+ subscription (either directly or indirectly through family sharing) is mandatory in order to benefit from a custom domain address.
- make it clear, when family members are added to the custom domain, that members that are not iCloud+ cannot benefit from the service.
- obviously: don't send verification link to someone that is not eligible to the service.
I've now successfully migrate my domain from Google Workspace.
Thanks to everyone that has contributed.