so the behavior of the pushbutton_callback() function is to run when the push button is pressed. so you are 99% there. get rid of the if statement and have the function be like
function pushbutton_Callback(hObject, eventdata, handles)
s = get(handles.editbox1, 'String');
set(handles.editbox2, 'String', s);
Since the callback will only run when the pushbutton is pressed there is no need to check the state of the button (unless you set the pushbutton to be a toggle button). if you do need to check the state of the button (ie as a togglebutton) you would use get(hangles.pushbutton,'value'). I'd read the documentation on pushbuttons/uicontrols to double check that last part.
