There are varieties of ways to do this, see which way will benefit China the most;
(1) To do this alone by the US only; (money, tech, etc)
(2) To do this by the US with some other countries without China;(joint interests, etc)
(3) To do this alone by China only; (money, tech, etc)
(4) To do this by the US,China and other countries;(joint interests, etc)
(5) To do this by other countries jointly without the US and China;
(6) To do this be each of the countries alone without joining each other.
I think that (4) will be likely. And some other reasonable concerns should be addressed as well:
1. How to prevent China's space military secrets to be spyed or monitored by the US or other partners? as this project goes by;
2. Who do what? Who pay what? Who own what?
3. Can China learn some advanced tech from this project?
4. Can China do it much faster and cost-effective without joining any other countries?
5. Will this project affect the China's National interest in the long run: such as obtaining natural resource from the Moon.