Found the solution on my own
For those who are experiencing the same issue.
1 - CMS Builder MUST be installed in the root directory of the web site. It is not evident in the documentation.
2 - the root directory MUST be 777 during installation (in my case public_html). Don't forget to get it back to a more standard 750 for example.
3 - the Connections directory MUST be 777 too.
And then, miracle, the installation runs.
After the installation, get Connections directory permissions back to 755.
The "files" directory created in root during installation must be chmod to 777.
Hope it helps