Just create the linked server connection and specify the user credentials in the code or in the "Security" page (when using the GUI).
EXEC master.dbo.sp_addlinkedserver @server = N'{FQDN_instancename}', @srvproduct=N'SQL Server'
EXEC master.dbo.sp_addlinkedsrvlogin @rmtsrvname=N'{FQDN_instancename}',@useself=N'False',@locallogin=NULL
,@rmtuser=N'{username}',@rmtpassword='########'