One of our website has URL like this : example.oursite.com. We decided to move our site with an URL like this www.oursite.com/example. To do this,
I am fairly certain that the hash/page anchor/bookmark part of a URL is not indexed by search engines, and therefore has no effect on your page ranking. Doing a google search for "inurl:#" returns zero documents, so that backs up my assumption. Links from external sites will be indexed without the hash.
You are right in that the hash part isn't sent to the server, so as far as I am aware, there isn't a good way to be able to create a redirection url with the hash in it.
Because of this, it's up to the browser to correctly manage the hash during a redirect. Firefox 3.5 appears to do this successfully. If you append a hash to a URL that has a known redirect, you will see the URL change in the address bar to the new location, but the hash stays on there successfully.
Edit: In response to the comment below, if there isn't a hash sign in the external URL for the part you need, then it is entirely possible to rewrite the URL. An Apache rewrite rule would take care of it:
RewriteCond %{HTTP_HOST} !^exemple\.oursite\.com [NC]
RewriteCond %{HTTP_HOST} !^$
RewriteRule ^/(.*) http://www.oursite.com/exemple/$1 [L,R]
If you're not using Apache, then you'll have to look into the server docs for something similar.