Hi,
It depends on what rendering engine you are using. If you are using VRay, for example, you can export an .abc file of the hair, create a VRay Proxy object in a new scene, import the .abc file into it and render. Other renderers have a similar option.
Another option is to install the demo version of Ornatrix on the other computer. Ornatrix will not ask for a license at render time and everything will work as long as you don't try to modify the hair using the demo version (The demo will reset the settings if you try to save the hair).
Jeordanis Figuereo (Product Designer. EPHERE Inc.)