Hi aurora,
The assessor will send their report, and your case file, to DWP several days after the appointment. So, unless you can get it to ATOS very quickly, it is likely that you will be best to send it directly to DWP. You can always send a copy (always keep the original yourself) to both places if you want to be certain it goes where it is needed.
Nothing on this board constitutes legal advice - always consult a professional about specific problems