Hi,
With server object model, we cannot copy the item from extranet farm to intranet farm.
To achieve this goal, we can use client object model.
As you are copying item from two different farms, then we need to set unique credential to be able to access each farm.
When getting item from the extranet farm, we need to use a unique credential with a user who can access the item in the list in the extranet farm.
When writing the item to the intranet farm, we need to use a unique credential with a user who can create item in the list in the intranet farm.
We can use the code below to set the unique credential:
NetworkCredential credentials = new NetworkCredential(username, pwd, domain);
ClientContext context = new ClientContext(http://thesitecollection);
context.Credentials = credentials;
More reference:
http://sharepointdragons.com/2012/04/20/authentication-when-using-the-sharepoint-client-object-model/
Thanks,
Victoria