What's the best/safe way to Transfer Files from a Server to another Server?

Hi,

I need to move all files from current server to a new one. What's the best/safe way to transfer All Files from current Server to a new one? The new server will have different URL domain.

I'm pretty sure all shared weblinks become invalid since the domain will be changed. Unless there's a way, something like WP migration plugin.

Preferably, the whole Filerun installation, including users and shared web links. 

Any add-on available?

Thanks