Bulk moving 300+ reports to a Public folder — will this break Dashboard references?

I need to move 300+ reports from one folder into a Public folder. These reports are referenced by several Dashboards, so preserving the report Ids is critical.

My plan is to do this via VS Code (Salesforce CLI / Metadata API):

so I want to confirm: does retrieve/move/deploy approach preserve the underlying Report Id

, or does it create a new record and leave the original (and any Dashboard references to it) orphaned? 

Thanks in advance!