You could do this if you have Nintex Workflow for Sharepoint.  You could set a workflow to create an item in another site.  You can set the workflow to start on either form creation or edit.  You can set the button on form 1 to be a save and continue.  Then set it to change a field item.  That would be the cause to start the workflow that creates the new item.  

I re explain please. I have the date the user enters; when he enters the date, the workflow start and calculate a date, then  it saves the two dates on  an element the list and save the calculate date on the next element of the list

So you would first setup a button that performs a Save and Continue function.

Then in the Advanced section, have it connected to a field that will tell your workflow to start.  Maybe a simple setting like if Value is 1 and a item is updated.

In your workflow, you will use Create item in another site.

Here you can select fields from the current list (form) and place them in the new list (form).  You must match compatible column types when doing this.  Hope this helps.

Yes, this is the example attached, i have the  field "date", i have the field "frequence" and i have the field  "date limite" and the field "ESC"  in my list called test.

I want that when  i enter the value of the date in the form it automatically fills the field "date limite"  by doing the calculation "date"+"frequence" and then create a new element in the list test  by writing the same ESC, the same frequency and the field "date" of the new element equals "date limite" of the previous element (on the same ESC)

this is a second image