Isso funciona para você?
touch --date "2017-05-01" /tmp/start
touch --date "2017-05-31" /tmp/end
find /path/ -type f -newer /tmp/start -not -newer /tmp/end -size +1G -exec mv "{}" /path/to/new/dir/ \;
você pode usá-lo como um script bash (por exemplo, scriptname.sh /path/to/search/dir /path/to/destination/dir
):
#!/usr/bin/env bash
touch --date "2017-05-01" /tmp/start
touch --date "2017-05-31" /tmp/end
find "$1" -type f -newer /tmp/start -not -newer /tmp/end -size +1G -exec mv "{}" "$2" \;
rm /tmp/start /tmp/end