Hello habit,
it's probably due to the fact that the calendar create an hidden input with the sufix _hidden in the ID.
So you can probably add a jquery script for setting this hidden field.
You can add this jquery script in the parameter of the field, at the bottom (orange down arrow), in the textarea "script".
Something like :
$("#my_field_start").on("change", function(){
$("#my_field_end_hidden").val($(this).val());
});
Best regads.
Lionel