Posting on a page in group if the URL is given

I am using spring social with my application and I have a requirement for posting on a particular page of the group. The user is expected to provide page of the group.(This group has like billions of page).Can user post on the page of a group in Facebook if the URL of the page is provided?.

Second question is : Is there a way where I can find the authentication I get using spring social is the same as the owner of the URL provided?


Thanks in advance :)