The reason you have had no reply is this thread is in the wrong section. This is for discussing third party editing tools for the game WC3. You are after the World Editor Help Zone where WorldEdit questions are asked and solved. A moval request has been sent.
You are not clear about the teleportation you are after. We know it is the instant movement from one point to another but you need to explain how you want this to relate to his attacks.
Anyway there are 2 general solutions.
1. A custom model animation. It could be possible to make him look like he teleports during his attack animation sequence using a custom model but he would always end back where he started.
2. Utalizing triggers. On every attack the unit is moved from its current position to another nearby position using a process to work out that position. SetUnitX/Y natives would need to be called to do this as they will not interrupt the current attack unlike other movement calls. Exact implimentation depends on your problem specification which currently is not clear.
You could also try contacting the actual map maker via E-mail or if he is registered to this site you could drop him off a Private (or even Public) message.
If triggered, you could also extract the JASS script driving the mechanics you are after directly from his map and port it to your own. If you do this, I advise giving the maker of that map credit as the trigger's source. You would need an MPQ editor and sufficient knowledge with JASS to understand potentially optimized code (poor readability).