TYPO3 Core

We have set up a reverse proxy and configured TYPO3 accordingly in Localconf.
reverseProxyHeaderMultiValue' => 'last',
reverseProxyIP' => 'xx.xx.xx.xx.xx',
reverseProxyPrefixSSL' => >'/intranet',
reverseProxySSL' => '*',

The URL in the browser is: domain.tld/intranet
This also works so far, but the backend of TYPO3 does not work at all after the login. It writes another "/intranet" every time..... Also the frontend does not work as soon as a login happens.
The URL to domain.tld/intranet/intranet/typo3/index.php?xxxxx is changed in the backend.
We solved it in such a way that we simply wrote a redirect in the htaccess. That if there is a "/intranet" in the URL, simply remove it. Nevertheless, we think that it is a TYPO3 error. Because now the following error is thrown in the backend when we want to edit a content element:
file_get_contents(/var/wwww/xxxx/html/typo3//intranet/typo3conf/ext/rtehtmlarea/Resources/Public/Css/Skin/jquery-ui-resizable.css

The /intranet is wrong there again! So somehow something is assembled wrong by TYPO3.