Clone / move / backup remotely

We normally only do Asterisk installations without any GUI but have a customer with FreePBX, version 2.4.0.0.

They are moving to a new location and already have a new server at that site. It’s a clean installation of FreePBX and basically they want that to be a clone of the current machine. This way they can switch within minutes when officially moving to the new location. Downtime should be kept to a minimal this way.

What is the best way to do this, I have SSH and HTTP access to both machines but we cannot physically access them.

Can I copy /etc/asterisk and some other directories or is it more complicated? I can imagine it is since there seems to be a MySQL etc. also.