Is it possible to tell Google's Webmaster Tools that our site hosted on www. has moved to a sub folder or perhaps even a subdomain?I know this is possible by using 301's but would appreciate if anyone can tell me if this can be done on Google's Webmasters Tools.
Moving site from its own domain to sub directory or subdomain - updating Webmaster Tools
domains;google search console;301 redirect;subdomain;migration
The tell Google you've moved feature is designed for old domain to new domain and does not support sub domains. This question has been asked various times on many forums across the internet, Google does not treat a domain to sub domain or any other moves on the same domain a complete move. You should proceed with a standard 301 which is more than enough to tell Google that your content has permanently moved. 