Let's go back to the other browser (Firefox in my case) where you logged in as User 2. Click on the little message icon beside User 1:
This will bring you to the new message page:
Go ahead and type a message, and hit SEND. Then, go back to Chrome where you're logged in as User 1. You should see a new message appear on the messages page from User 2:
And if you click on the message, you should be able to read the message content: ...