Can the trooper move forward and just with some part of the baze vault over the parapet , and then go back and finish his move on a normal surface (as in attached image )?
There is nothing in the rules that prevents it, and I do think IJW has answered that you can vault up a parapet as long as you don't have any over-hang outside the building (in discussions about using squeeze rules to "Lean Out") https://forum.corvusbelli.com/threads/move-over-edge-to-look-below.38296/page-4#post-387480 (It's a bit confusing because IJW is answering different lines of question)
I think the ambiguity here could lie in the original rule, as we are used to say "vault" but the actual text is "move over any scenery..". The point is that -over- in English can mean both -upon- and -across-. The first meaning would suggest a clear "yes, you can", the second meaning would open to the discussion if going back can technically be a valid use of moving across. As far as I can see by English not being my first language.
Based on extensive discussion in several threads read "over" as "upon" not "across". (search the forum for inane, IJW and vault).
