Can I report my patent fraud?

Of course.

First of all, it must be clear that the State Patent Office is a patent examination unit and probably cannot report it in the name of fraud. Secondly, it is not clear whether two people are applying for the same patent or something else.

Where two people apply for the same patent, the patent right shall be granted to the person who applied first. The inventor may invalidate the patent of the other party by invalidation.