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if I move a file between 2 folder, does synchronization move the file or delete/past it?

I Have some folders with hundred pictures in the primary HDD and I sync in 2 different secondary hard drives.
They are still unorganized and I need to separate pictures in folders.

If I Move some files in the main hdd between two folders, does exist a software that in the secondary hdd moves actually the files contained in the secondary HDD?
I want to avoid the software deletes it from the first folder of the second HDD and copy from first hdd and paste in the new folder of second hdd


edit:
I add some infos and excuse me for my poor English.

I usually use win11. I mainly use FreeFileSync as sync software.
I tried to search in the forum an answer to my question but without any result. I find this forum exctly during a search.

Now I’m trying to explain why I want to avoid the simple sync.
I didn’t make yet a real backup of folders until I make order between pictures. I’m just synchronising them to do a simple, rough and temporary backup. If (for any reason) a file from first HDD is damaged/modified/etc and it is copied to secondary HDD, I will lose the intact file. is this a right reason? is there any alternative?