Update one SQL Server from another

We have 2 separate servers one has SQL Server 2012 and the other with SQL Server 2005.

I want to fetch data from 2012 and update to 2005 thru a SQL query.

I have only access rights for 2012 server.

Thanks in advance

Without access rights to the 2005 Server, you cannot update data in that server. That is the way it shoudl be, right? Otherwise, anyone would be able to mess with your data.

I've full access for 2005 Server, only 2012 has access rights

There are several ways to send data from one server to another. Linked Servers, SSIS, Replication etc. If you don't need near-real time syncing of the data, I would suggest SSIS. For simple cases, you can use import-export wizard to port the data, and as part of that, create an SSIS package, which then can be run on a schedule if needed.