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You don't need a shell window to move a file. Vim has an integrated file explorer you can use for file operations. Vim's file explorer can be acessed using :Explore in normal mode (or just enter :e. which is a command to edit the current directory). It should list files in the current directory.
How to
In normal mode type :Sex to split the current window and open Explore above it. Or :Sex! to split vertically. If the current window has no file, the current directory is opened (as shown by :pwd).
Navigate to a file name using hjkl, or arrow keys.
Press R to rename a file.
A prompt is shown that the selected file will be moved (renamed), and the original full path for the destination is shown. Change that path as wanted and press Enter to move the file, or Esc to cancel.