I think there is a small confusion here. There are 2 things inside the hasp. Simplemindedly, the factory programmed things (encoding algorithms/commands etc) and the custom data (those that developer programmed inside the embedded memory).

What you have dumped? The factory programmed stuff or the memory data? If you have dumped the factory programmed stuff as far as i know you cant rewrite them in another hasp and have an exact copy of the original hasp. That dump information can only be used to create an emulator, a software that will stay in the memory and behave like the original hasp, like reply to commands, encode/decode data etc.

On the other hand, if you need to write the memory data, you need the access codes that supplied from the hasp manufacturer to the developer (2 or 4 passwords).

Anyway, duplicating hasp is not an easy story and there are only some crackers that are able to easily create hasp copies (using an emulator of course).