What we need is to install SharePoint Designer Service Pack 1
We downloaded SharePoint Designer Service Pack 1 and we must have an executable like the following SharePoint Designer Service Pack 1
We run it and wait for it to finish installing
At the end it will ask us to restart the computer, click on ” Yes ” and wait for the computer to restart.
After the computer finishes restarting, we open SharePoint Designer and click on “ Open site ”, the following window will appear.
We select the site that we had already tried to open previously, click on the “Open” button , it will request username and password, it will begin to Communicate with the Web service and finally it will open the Site in Sharepoint Designer.
In this way we solve the problem when wanting to open SharePoint Online sites in SharePoint Designer and it says that they do not have Permissions.