Let's suppose I have a folders in the source system: AB1, AB2, AB3.
And I have the same folder names AB1, AB2, AB3 in the destination system.
I want to move AB1 files to AB1 and AB2 files AB2 and AB3 files to AB3.
When you say it is a different system, I suppose it is into another computer and you want to copy by network, right?
There exists a lot of ways to make this copy, to suggest one which is better to you, you need be more specific of the systems and the copy process.
Example: you just want to move full data into a system to another, or you need update frequently this files? Is a single move copy? Size of this copy? you need check data integrity at end? need be fast and doesn't care with cryptography? Or need by with cryptography? Will be made by script or by hand?
If we are talking about transfer into two unix/linux, then you can use tar to data compress, and send it with scp which use a ssh connection to transfer your data, and then decompress there into destiny folder that will insert the new data respecting its struct, after that you remove the old content, because it is more safe this way.
Or perhaps you should use rsync to copy data, I like it because it can copy only changed files, and it transfer data through ssh too.
It's possible to mount a ssh conection with sshfs and use like a folder, which means you can use cp.
Because they copy data through ssh is more slow than make a non cryptographed, but is safe and simple to do.
If it's ok to you to copy without cryptography, you can mount the other file system into your system and then copy with cp, between linux/windows with samba, and linux to linux I suggest NTF, the NTF with async copy is fast.
I never would do a direct move through network, instead I would copy and after the copy remove content from the source system.