Nginx proxy domain to another domain with no change URL

Solution 1:

You set:

proxy_set_header Host $host;

You want:

proxy_set_header Host connect2.domain.ru;

Solution 2:

Telepathy about port 8080 has been turned off, because you don't show us the full config.

server {
    listen 80;
    server_name connect3.domain.ru www.connect3.domain.ru;

    location / {
        proxy_pass http://connect2.domain.ru;
        proxy_set_header Host connect2.domain.ru;
    }
}