I'm sorry for the babble above but the source of errors are too many.
The previous post the problem was php (e.g. phpMyAdmin).

The final working setup:

src/http/ngx_http_header_filter_module.c:
#if (NGX_HTTP_SSL)
if (c->ssl || port == 443) {
*b->last++ ='s';
}
#endif

In order to work nginx needs this config:
server {
listen 127.0.0.1:443 proxy_protocol;
port_in_redirect on;

stunnel.conf:
[tls to http]
sni = tls:*
connect = 127.0.0.1:443
protocol = proxy

fastcgi_params:
# http://tyy.host-ed.me/pluxml/article4/port-443-for-https-ssh-and-ssh-over-ssl-and-more
fastcgi_param HTTPS "on";
fastcgi_param SERVER_PORT "443";

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