Simple answer is no, not without restoring all data back into exchange and then resetting up your PF archiving from scratch.

What Wayne said.....

Moved Items checking aka Modifiable Metadata exists only for mailbox archives, so moving archived items around a mailbox can result in the items being moved around in the archive too (new feature in EV 8).

This doesn't exist for public folders.

So, there is no solution for my problem?

I found a workaround by copy items back to Public Folders through Archive Explorer, delete archive and reschedule it.
But this is not efficient if you have thousands of items.

There sort of is,

You could select all the items in the Public Folder and then click restore.....

Once all is restored into Exchange re-setup your Public Folder archiving again how you like and re archive all the data.

If you cant do that you cant really achieve what you want without getting someone to write a tool for you.

The think is I cannot restore them from outlook because we do not leave shortcuts after archiving.
So, I assume the only way is by Archive Explorer.