Meagan Longoria has a workaround for how you cannot move a file using Azure Data Factory:
But at this time ADF doesn’t support that. You can copy a file with a copy activity, but you cannot actually move (i.e., copy and delete).
Luckily, we had a workaround for our situation. If you tell ADF to copy data to a file that already exists in the specified location in the data lake, it will overwrite the existing file. We made sure the file name is always the same for each table in the staging area so there is always only one file per table.
Read on for the full details on this workaround. Also, vote on this feedback item if you want the ability to move files instead of just copying them.