It does not appear that you can move code attachments directly using AGO Assistant. When you move the web mapping application, does the code attachment go with it? If it doesn't, how do you suggest moving the application along with the code attachment?
You can move the code attachment by following the next steps :
1) Download the code attachment in your disk as a zip file;
2) Access to the Webapp by using the sharing API
3) Select AddItem
4) Ensure to enter the right parameters :
5) Click Add Item