In a modern SharePoint site (or in MS Teams) you can move or copy files with the build in functionality. There is less need for migration tooling. The problem is how do you move/copy a file if it is not available in the pop up screen?
There is a source site with one file that you want to move
In the toolbar you select Move to…
…and the pop screen appears. If the target site is not available in Quick access (1) you can try to find it under More places (2)
So what to do when the target site is still not there?
You should navigate to the target site and choose Add shortcut to OneDrive
Then select Move to again in the source site and select My files in the pop up
The document library of the target site is there! Select it and…
…choose Move here
Navigate to the Target site and check that the file is there.
Hope this helps!