Hi Pierre,
There is a function you can add after your "Open/Create/Replace" vi called "Set File Position" which will begin writing at a desired position (in this case you want the end of the original file).
There are basic instructions and examples on how to use it in this forum post (see the third post, they talk about a few other things further in the thread):
http://forums.ni.com/t5/LabVIEW/Append-text-to-end-of-file/td-p/517823
Ash Beigi
Academic Technical Sales Representative
National Instruments - Electronics Workbench Group
