What are the official procedures to migrate all web sites related files from an ISPConfig 3.2.5 host to another ISPConfig 3.2.5 host? Both hosts will be up simultaneously for a certain period of time.
Probably purchase and use the migration toolkit. You can do it manually as well, though it would likely save time to use the migration tool. The manual procedure is basically: create resellers/clients with appropriate limit templates, add domains, create the websites and databases, then copy the website files over and set ownership/permissions (exactly what files to copy can vary, but typically it's just the "web" and maybe "private" folder of each website - though you could also have files under a web user home dir, or other locations - vhost alias and subdomains will also have their own directories), and dump/copy/load all databases.