There are certain limitation when copying the database from one server to another (remotely).
So you have to follow the steps to completely transfer the database from one server to another with same identities and along with constraints.
To say in short, Generate Script of database i.e. Right click database > Tasks > Generate Scripts > Select database > Mark these true: Triggers, Indexes, Primary & Foreign Keys and other if any. > Choose Object Types: Mark all true except for User (you can create users on new server later on manually). > Select all the Tables, SP, and other Objects > Script to New Window or Files (as you wish) > Finish.
Generate Script to 'Create Database' and run it on server.
Run the step 1. Script on the new server, check that the new database is selected in query window.
Disable all the constraints on new server > EXEC sp_msforeachtable "ALTER TABLE ? NOCHECK CONSTRAINT all"
I think using wizard is speedy so, Use Database Export Wizard from the old database server to transfer the data from old database server to new database server.
Again, Enable all the constraints on new server > EXEC sp_msforeachtable @command1="print '?'", @command2="ALTER TABLE ? WITH CHECK CHECK CONSTRAINT all"
PS: The version does not matter as you have to transfer the database supposing to be in current version in your case SQL Server 2008, and after copying the database you can change the version of database.
Database Properties > Select a page: 'Options' > Compatibility level > select the version from drop down.