Yes.
The HTTP_REFERER is data passed by the client. Any data passed by the client can be spoofed/forged. This includes HTTP_USER_AGENT.
If you wrote the web browser, you’re setting and sending the HTTP Referrer and User-Agent headers on the GET, POST, etc.
You can also use middleware such as a web proxy to alter these. Fiddler lets you control these values.
If you want to redirect a visitor to another website and set their browser’s referrer to any value you desire, you’ll need to develop a web browser-plugin or some other type of application that runs on their computer. Otherwise, you cannot set the referrer on the visitor’s browser. It will show the page from your site that linked to it.
What might be a valid solution in your case would be for you to load the third party page on the visitor’s behalf, using whatever referrer is necessary, then display the page to the user from your server.