Bash script - Delay cp command until after file write is complete
Lock File

Consider creating a lock to note the ongoing copy, see lock your script (against parallel run):

#!/bin/sh

# Path to a lock folder
LOCK_PATH="/tmp/copying.lock"

# Ensure the lock is removed should the copy fail
trap 'rmdir "/tmp/copying.lock"; exit' 1 6 15

if mkdir "$LOCK_PATH"; then
    # Lock file did not exist and was created

    # Perform commands
    cp /Folder1/*.mov /Folder2/
    cp /Folder1/*.mov /Folder3
    rm /Folder1/*.mov   

    # Remove the lock
    rmdir "$LOCK_PATH"
fi


The script above only copies if no folder exists at /tmp/copying.lock.

Copy and Move

Instead of copying directly to the final location, consider making the copy to a temporary location. Then move the files. A move is fast, tends to be atomic, and less likely to damage the files.

Alternatively, you could copy using a tool like rsync which includes flags to help protect against these problems.