Does this mean I cannot report this fake nomination?

In a local chat group, a user has admitted and even posted a screenshot of the fake nominations that he has submitted using the same picture in our city and in another city in a different state.
I know the username but NOT the coordinates of them. Does this mean that the report will not go through?

You can certainly report abuse anonymously at the following link:

Just provide as much information as you can. I would make sure to include their username in whichever game they submitted these nominations with, as well as the screenshots they posted. These will help Niantic in locating the nominations they have submitted that are fake, and remove them.

I have followed the link, but the first step requires you to enter the coordinates, and then it says that it will ask for pictures on the follow up e-mail.
I’m just afraid that the process will stop there because of me being unable to provide coordinates.

Again, just provide as much information that you can. More is helpful, but if you don’t have all the information, you can still submit. You may just want to put NA in for the sections that you don’t know.